# Nash equilibrium

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pages: 1,535 words: 337,071

Networks, Crowds, and Markets: Reasoning About a Highly Connected World by David Easley, Jon Kleinberg

If each player believes that the other player will actually play a strategy that is part of a Nash equilibrium, then she is willing to play her part of the Nash equilibrium. Let’s consider the Three-Client Game from the perspective of Nash equilibrium. If Firm 1 chooses A and Firm 2 chooses A, then we can check that Firm 1 is playing a best response to Firm 2’s strategy, and Firm 2 is playing a best response to Firm 1’s strategy. Hence, the pair of strategies (A, A) forms a Nash equilibrium. Moreover, we can check that this is the only Nash equilibrium. No other pair of strategies are best responses to each other.1 This discussion also suggests two ways to find Nash equilibria.

To prove that the set of Nash equilibria remains the same through one round of deletion, we need to show two things. First, any Nash equilibrium of the original game is a Nash equilibrium of the reduced game. To see this, note that otherwise there would be a Nash equilibrium of the original game involving a strategy S that was deleted. But in this case, S is strictly dominated by some other strategy S . Hence S cannot be part of a Nash equilibrium of the original game: it is not a best response to the strategies of the other players, since the strategy S that dominates it is a better response. This establishes that no Nash equilibrium of the original game can be removed by the deletion process.

We can now ask whether there is a Nash equilibrium for this richer version of the game. Equilibrium with Mixed Strategies. We define a Nash equilibrium for the mixed- strategy version just as we did for the pure-strategy version: it is a pair of strategies (now probabilities) so that each is a best response to the other. 6.7. MIXED STRATEGIES 187 First, let’s observe that no pure strategy can be part of a Nash equilibrium. This is equivalent to the reasoning we did at the outset of this section. Suppose, for example, that the pure strategy H (i.e. probability p = 1) by Player 1 were part of a Nash equilibrium. Then Player 2’s unique best response would be the pure strategy H as well (since Player 2 gets +1 whenever he matches).

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The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling by Adam Kucharski

Such approaches can be particularly important in games like poker, which can have more than two players. Recall that, in game theory, optimal strategies are said to be in Nash equilibrium: no single player will gain anything by picking a different strategy. Neil Burch, one of the researchers in the University of Alberta poker group, points out that it makes sense to look for such strategies if you have a single opponent. If the game is zero-sum—with everything you lose going to your opponent, and vice versa—then a Nash equilibrium strategy will limit your losses. What’s more, if your opponent deviates from an equilibrium strategy, your opponent will lose out.

The same problem crops up in poker. As well as causing inconvenience, it can cost players money. Three poker players could choose Nash equilibrium strategies, and when these strategies are put together, it may turn out that two players have selected tactics that just so happen to pick on the third player. This is why three-player poker is so difficult to tackle from a game theory point of view. Not only is the game far more complicated, with more potential moves to analyze, it’s not clear that hunting for the Nash equilibrium is always the best approach. “Even if you could compute one,” Michael Johanson said, “it wouldn’t necessarily be useful.”

But if your opponent has flaws—or if there are more than two players in the game—you might want to deviate from the “optimal” Nash equilibrium strategy and instead take advantage of weaknesses. One way to do this would be to start off with an equilibrium strategy, and then gradually tweak your tactics as you learn more about your opponent. Such approaches can be risky, however. Tuomas Sandholm at Carnegie Mellon University points out that players must strike a balance between exploitation and exploitability. Ideally, you want to exploit, taking as much as possible from weak opponents, but not be exploitable, and come unstuck against strong players. Defensive strategies—such as the Nash equilibrium, and the tactics employed by Dahl’s poker bot—are not very exploitable.

Economic Origins of Dictatorship and Democracy by Daron Acemoğlu, James A. Robinson

A player chooses a strategy to maximize this function where a strategy is a function that determines which action to take at every node in which a player has to make a decision.3 A strategy here is simply how to vote in different pairwise comparisons. The basic solution concept for such a game is a Nash equilibrium, which is a set of n strategies, one for each player, such that no player can increase his payoff by unilaterally changing strategy. Another way to say this is that players’ strategies have to be mutual best responses. We also extensively use a reﬁnement of Nash equilibrium – the concept of subgame perfect Nash equilibrium – in which players’ strategies have to be mutual best responses on every proper subgame, not just the whole game. (The relationship between these two concepts is discussed in Chapter 5.)

Therefore, the predictions of this model can be summarized by the corresponding Nash equilibrium, in which each party chooses the policy that maximizes its utility given the policy of the other party. Nash equilibrium policy platforms, (q A∗ , q B∗ ), satisfy the following conditions: q A∗ = arg max {P (q A , q B∗ ) (R + WA (q A )) + (1 − P (q A , q B∗ ))WA (q B∗ )} q A ∈Q and, simultaneously: q B∗ = arg max {(1 − P (q A∗ , q B )) (R + WB (q B )) + P (q A∗ , q B )WB (q A∗ )} q B ∈Q Intuitively, these conditions state that in a Nash equilibrium, taking q B∗ as given, q A∗ should maximize party A’s expected utility.

Thus, in this model, a subgame perfect Nash equilibrium would be a set of n + 2 strategies, one for each of the political parties and one for each of the n voters, which would determine which policies the parties offered and how individuals would vote. If such a set of strategies constituted an equilibrium, then it would have the property that neither party and no voters could improve their payoff by changing their strategy (e.g., by offering a different policy for parties or voting differently for citizens). In the present model, however, we can simplify the description of a subgame perfect Nash equilibrium because, given a policy vector (q A , q B ) ∈ Q × Q, voters simply vote for the party offering the policy closest to their ideal point and, because preferences are single-peaked, the MVT implies that the winner of such an election is determined by (4.2).

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Licence to be Bad by Jonathan Aldred

In the original Prisoner’s Dilemma story, the reasoning described earlier implies that both players should confess. And this outcome is a Nash equilibrium: if your partner confesses, you do best by confessing too. So the blame for the damaging non-cooperation nurtured by this reasoning may seem to lie with John Nash’s equilibrium idea. But – although millions of students in social science, philosophy, law and biology are today introduced to game theory via the Prisoner’s Dilemma and its Nash equilibrium ‘solution’ – the Nash equilibrium idea is not driving the outcome here. There is a more basic logic at work: regardless of what the other player does, your best action is to confess.

And without this assumption, the explanation for why we get locked into non-cooperative situations disappears. Put another way, game theory says we will end up in a Nash equilibrium, but it does not explain which equilibrium – cooperative, non-cooperative or otherwise. It is a Nash equilibrium that everyone drives on the same side of the road, and there are two equilibria: everyone drives on the left, and everyone drives on the right. Game theory has little to say about which equilibrium will emerge, and why it differs across countries. Likewise, the QWERTY layout for keyboards is a Nash equilibrium: if everyone is using QWERTY to type, and almost all keyboards are manufactured with QWERTY, then you should learn to type using QWERTY too, and new keyboards will be made with that design.

But it matters when the stakes are lower too: when Samsung and Apple play games with each other in the pricing and design of new smartphones, many outsiders try to predict what will happen – consumers, regulators and chip manufacturers all have an interest. In short, we look to game theory for an answer, a solution, comprising a prescription of how to play, or a prediction of what will be played, or both. Ever since Nash’s 1950 paper, Nash equilibrium has been the basis of that answer: simultaneously a prediction of what a stable outcome must look like and a prescription of how to play. Nash equilibrium bears the mark of a real intellectual breakthrough – an idea that had not occurred to anyone before Nash yet one that with hindsight seems entirely obvious. Together, von Neumann, Morgenstern and Nash had triggered a revolution in our thinking about human interaction.

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Therefore, via actions such as quality score and minimum bids, the search engine acts to keep auctions stable. One of best-known points of stability is the Nash equilibrium, which is a set of bids so that, given these bids, no advertiser has an incentive to change their bidding behavior. There is always at least one Nash equilibrium set of bids for a GSP auction, and among the equilibrium, there is always one that maximizes total advertiser valuation (i.e., all advertisers get the most from their bids). In other words, the GSP auction always has an efficient Nash equilibrium. The Serious Game of Bidding 197 Potpourri: The Nash Equilibrium [3 [30, 30, 331] 1] is a concept in game theory strategy.

Stability is a key component for online auctions, such as those associated with sponsored search. A key component of the Nash Equilibrium is that all players must know the strategies of the other players. Although not really possible in a sponsored-search auction, advertisers can get a close approximation of the other advertiser’s strategies, which is good enough. The Nash Equilibrium entered pop culture with the 2001 American movie, A Beautiful Mind, directed by Ron Howard and starring Russell Crowe, Ed Harris, and Jennifer Connelly. A full-information (i.e., perfect information) Nash equilibrium is often used for modeling sponsored-search auctions, even though the sponsored-search auction does not operate under conditions of perfect information.

., perfect information) Nash equilibrium is often used for modeling sponsored-search auctions, even though the sponsored-search auction does not operate under conditions of perfect information. The argument for the assumption of a full-information Nash equilibrium is that even if the bidders do not know exactly what the other advertisers are bidding, there is the possibility of updating bids until the auction gets to the best level, meaning that the resulting Nash equilibrium is about the same as if there had been full information in the first place [6]. The advantage of the GSP auction is that it has a pure-strategy Nash equilibrium and avoids a pattern of constant updates in bids [22]. The following mathematical model captures the essential features of sponsoredsearch auctions, based on integration from multiple sources [10, 28, 32, 33, 29].

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Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian, Tom Griffiths

Mixed strategies appears as part of the equilibrium in many games, especially in “zero-sum” games, where the interests of the players are pitted directly against one another. every two-player game has at least one equilibrium: Nash, “Equilibrium Points in N-Person Games”; Nash, “Non-Cooperative Games.” the fact that a Nash equilibrium always exists: To be more precise, ibid. proved that every game with a finite number of players and a finite number of strategies has at least one mixed-strategy equilibrium. “has had a fundamental and pervasive impact”: Myerson, “Nash Equilibrium and the History of Economic Theory.” “a computer scientist’s foremost concern”: Papadimitriou, “Foreword.” “Give us something we can use”: Tim Roughgarden, “Algorithmic Game Theory, Lecture 1 (Introduction),” Autumn 2013, https://www.youtube.com/watch?

The link between Nash equilibria and PPAD was established in Daskalakis, Goldberg, and Papadimitriou, “The Complexity of Computing a Nash Equilibrium” and Goldberg and Papadimitriou, “Reducibility Between Equilibrium Problems,” which was then extended to two-player games by Chen and Deng, “Settling the Complexity of Two-Player Nash Equilibrium,” and then further generalized in Daskalakis, Goldberg, and Papadimitriou, “The Complexity of Computing a Nash Equilibrium.” PPAD stands for “Polynomial Parity Arguments on Directed graphs”; Papadimitriou, who named this class of problems in “On Complexity as Bounded Rationality,” insists any resemblance to his name is a coincidence.

In one of the seminal results in game theory, the mathematician John Nash proved in 1951 that every two-player game has at least one equilibrium. This major discovery would earn Nash the Nobel Prize in Economics in 1994 (and lead to the book and film A Beautiful Mind, about Nash’s life). Such an equilibrium is now often spoken of as the “Nash equilibrium”—the “Nash” that Dan Smith always tries to keep track of. On the face of it, the fact that a Nash equilibrium always exists in two-player games would seem to bring us some relief from the hall-of-mirrors recursions that characterize poker and many other familiar contests. When we feel ourselves falling down the recursive rabbit hole, we always have an option to step out of our opponent’s head and look for the equilibrium, going directly to the best strategy, assuming rational play.

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Prisoner's Dilemma: John Von Neumann, Game Theory, and the Puzzle of the Bomb by William Poundstone

Flood and Dresher wondered what John Nash would make of this. Mutual defection, the Nash equilibrium, occurred only fourteen times. When they showed their results to Nash, he objected that “the flaw in the experiment as a test of equilibrium point theory is that the experiment really amounts to having players play one large multi-move game. One cannot just as well think of the thing as a sequence of independent games as one can in zero-sum cases. There is too much interaction, which is obvious in the results of the experiment.” This is true enough. However, if you work it out, you find that the Nash equilibrium strategy for the multi-move “supergame” is for both players to defect in each of the hundred trials.

It’s necessary to put two numbers in each cell of the game table. The first gives the payoff to the “row player” (the one who chooses the row of the outcome). The second number in each cell is the payoff of the “column player.” No longer can we assume that one player’s gain is another’s loss. Some cells have a higher combined payoff than others. The Nash equilibrium solution is for both players to choose their strategy 2 (lower right cell, boldface). Obviously the row player is satisfied with this, for he wins 5 points, the most he could win under any circumstances. But this outcome can be justified to the column player as well. Playing Monday-morning quarterback, given that the row player chose strategy 2, the column player cannot regret having chosen his strategy 2.

These equilibrium points can have “strange and undesirable properties,” as Philip D. Straffin, Jr., put it (1980). The above example was chosen to show a game where the equilibrium point solution clearly makes sense. Other times, equilibrium point solutions appear less inevitable than the solutions of zero-sum games. In fact, sometimes Nash equilibriums appear to be distinctly irrational. We will explore the consequences of this in the following chapters. 1. “The Rand Hymn” words and music by Malvina Reynolds. © Copyright 1961 Schroder Music Co. (ASCAP). Renewed 1989 by Nancy Schimmel. 2. But Flood doubts that even von Neumann could have calculated that fast.

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A Beautiful Mind by Sylvia Nasar

Nash’s theory predicted that both players would play their dominant strategies, even though playing their dominated strategies would have left both better off. Though Williams and Alchian didn’t always cooperate, the results hardly resembled a Nash equilibrium. Dresher and Flood argued, and von Neumann apparently agreed, that their experiment showed that players tended not to choose Nash equilibrium strategies and instead were likely to “split the difference.” As it turns out, Williams and Alchian chose to cooperate more often than they chose to cheat. Comments recorded after each player decided on strategy but before he learned the other player’s strategy show that Williams realized that players ought to cooperate to maximize their winnings.

In the early 1990s, I was an economics reporter at the New York Times. I was interviewing a Princeton professor about some trade statistics when he mentioned a rumor that a “crazy mathematician” who hung around the math building might be on the short list for a Nobel prize in economics. “You don’t mean the Nash of the Nash equilibrium?” I asked. He told me to call a couple of people in the math department to learn more. By the time I put down the phone, I realized that this was a fairy tale, Greek myth, and Shakespearean tragedy rolled into one. I didn’t write the story immediately. Lots of people wind up on short lists for the Nobel and never win, so writing about him in a newspaper would have been an invasion of privacy.

Individual rationality and self-interest, not common agreement on some collective good, seemed sufficient to create a tolerable order. The leap was a short one, from his observations of his hometown to his focus on the logical strategy necessary for the individual to maximize his own advantage and minimize his disadvantages. The Nash equilibrium, once it is explained, sounds obvious, but by formulating the problem of economic competition in the way that he did, Nash showed that a decentralized decision-making process could, in fact, be coherent — giving economics an updated, far more sophisticated version of Adam Smith’s great metaphor of the Invisible Hand.

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Model Thinker: What You Need to Know to Make Data Work for You by Scott E. Page

Suppose that the existing firm chooses to compete if the entrant enters. If the entrant knows this, the entrant would not enter, as doing so would produce negative profits. This set of actions, the entrant choosing to not enter and the existing firm planning to compete if the entrant did enter, are a Nash equilibrium. However, this is not the only Nash equilibrium, nor is it the most likely outcome. There is a second equilibrium in which the entrant chooses to enter the market and the existing firm accepts the entrants move and does not compete. To select among these two equilibria, we apply a refinement criterion. In sequential games, a common refinement chooses the subgame perfect equilibrium.

Their utility can be written as follows: Utility(M) = B − θ · M where B denotes the maximal benefit, and θ is a congestion parameter. The remaining (N − M) people abstain and receive utility of zero.9 Socially optimal: M = Utility = Nash equilibrium: M = Utility() = 0 In the socially optimal solution, the number of people who use the resource equals the maximal possible benefit divided by twice the congestion parameter. Those findings align with our intuition. The number of people who use the resource should increase with the maximal benefit and decrease with greater congestion effects. In the Nash equilibrium solution, exactly double the socially optimal number of people use the resource. Congestion becomes so severe that no one receives any benefit.

That assumption would capture resources like roads, in which the first few other users have no effect on an individual’s benefit and in which at some point the resource is so overcrowded as to be useless. 9 The total utility from M people using the resource equals (B − θ · M). Taking the derivative with respect to M and setting it equal to zero equals (B − 2Mθ) = 0. Solving gives M = . To solve for the Nash equilibrium, we set the value of abstaining equal to zero. People use the resource until the benefit equals the outside option: M = . 10 Note: we set the maximal benefit B equal to the population size N to reduce the number of variables. To solve for the socially optimal outcomes and Nash equilibrium, we first note that total utility equals (N − M) · M + 3(N − (N − M)) · (N − M), which reduces to 4(N − M)M. Taking the derivative with respect to M gives 4N −8M = 0.

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Explaining Humans: What Science Can Teach Us About Life, Love and Relationships by Camilla Pang

Among game theory’s many ideas and applications is the Nash equilibrium. This is the concept that, in any finite game, there is a point of balance where all players can take the decision that is in their individual best interests – and that none of them would change that course if the other players’ tactics were revealed to them. In other words, equilibrium is reached where individual and collective interests converge and there is no further optimization to be achieved. A proper compromise. A solution everyone is happy with: be it a playlist, a holiday destination or the food for a picnic. The Nash equilibrium and its offshoots are used in a wide range of fields, both to understand how aligned or opposed players will approach a particular problem, and to shape policy or decisions which seek to influence the choices of certain players.

It’s a convergence I have always sought to find between myself and other people – though I’m also fascinated when I can’t, and to work out why that is. What’s more, whenever a particular group of people changes – be that in its membership or the preferences of the same individuals – then the nature of the Nash equilibrium will evolve in turn. How does this help us as we tiptoe across the burning coals of social etiquette? Well, to start with it encourages us to look beyond our own perception of certain events, and to put ourselves in the shoes of the other player. Because game theory is ultimately about interdependence – how our outcome depends in part on someone else’s choices – we can’t just live in our own heads, or base decisions on our own judgement.

We need to anticipate how the other person will respond to our question, ice-breaking remark or suggestion. Is what we are about to say or do going to give them the scope to be offended or upset? Based on what we know about the player in question, the context of the interaction and our own ability to execute, how likely is our next move to achieve the desired outcome? What is the effective Nash equilibrium of the situation, in which everyone gets what they want without having to change course? If ABM allows you to understand the implied etiquette of a given system, game theory is the technique to model your subsequent decisions, aligning them with both your own ideal outcomes, and the choices others are making in parallel or response.

Super Thinking: The Big Book of Mental Models by Gabriel Weinberg, Lauren McCann

Hence the dilemma: do you risk their betrayal, or can you trust their solidarity and emerge with a small sentence? The dual betrayal with its dual five-year sentences is known as the Nash equilibrium of this game, named after mathematician John Nash, one of the pioneers of game theory and the subject of the biopic A Beautiful Mind. The Nash equilibrium is a set of player choices for which a change of strategy by any one player would worsen their outcome. In this case, the Nash equilibrium is the strategy of dual betrayals, because if either player instead chose to remain silent, that player would get a longer sentence. To both get a shorter sentence, they’d have to act cooperatively, coordinating their strategies.

To both get a shorter sentence, they’d have to act cooperatively, coordinating their strategies. That coordinated strategy is unstable (i.e., not an equilibrium) because either player could then betray the other to better their outcome. In any game you play, you want to know whether there is a Nash equilibrium, as that is the most likely outcome unless something is done to change the parameters of the game. For example, the Nash equilibrium for an arms race is choosing a high arms strategy where both parties continue to arm themselves. Here’s an example of a payoff matrix for this scenario: Arms Race Payoff Matrix: Economic Outcomes B disarms B arms A disarms win, win lose big, win big A arms win big, lose big lose, lose As you can see, the arms race directly parallels the prisoner’s dilemma.

Here’s an example of a payoff matrix for this scenario: Arms Race Payoff Matrix: Economic Outcomes B disarms B arms A disarms win, win lose big, win big A arms win big, lose big lose, lose As you can see, the arms race directly parallels the prisoner’s dilemma. Both A and B arming (the lose-lose situation) is the Nash equilibrium, because if either party switched to disarming, they’d be worse off, enabling an even poorer outcome, such as an invasion they couldn’t defend against (denoted as “lose big”). The best outcome again results from being cooperative, with both parties agreeing to disarm (the win-win situation), thus opening up the opportunity to spend those resources more productively.

Gaming the Vote: Why Elections Aren't Fair (And What We Can Do About It) by William Poundstone

Myerson and Weber ended up collaborating on a 1993 article, "A Theory of Voting Equilibria." In Weber's words, 'This is the paper that, I believe, makes the strongest theoretical case for approval voting." The publication invokes another idea with roots in the cold war, the "Nash equilibrium." As a RAND consultant, mathematician John Nash (of A Beautiful Mind fame) proposed a particular kind of solution to the "games" of nuclear deterrence or voting or anything else, A Nash equilibrium is an outcome where everyone is satisfied with his or her decision, given what everyone else did. No one has any regrets about doing what he did. In the case of voting, this means that all the voters are happy with the way they voted (though not necessarily happy with the election's outcome).

Spoilers and vote splitting lead to outcomes that are not Nash equi- 214 Bad Santa libria. If I cast a plurality vote for Nader, thinking that Gore is sure to win, and then Bush wins because of my vote and I kick myself for not having voted for Gore, my vote would not be part of a Nash equilibrium. It goes without saying that 99-plus percent of voters have never heard of a Nash equilibrium. No matter; opinion polls tend to herd voters into equilibrium outcomes. What worries Saari is roughly this. r go into the voting booth believing that the race is between Bill Clinton and George H. W. Bush. I cast an approval vote for whichever front runner I like better.

A pact is credible only when both sides can assure themselves that no one has an incentive to violate the pact-in other words, when it's a Nash equilibrium. In that case, you don't need a pact. Everyone can be expected to vote in his own best interests anyway. Myerson and Weber treat a hypothetical race similar to Buckley v. Goodell v. Ottinger. Preelection polls would help voters decide which of the two "clone" candidates is stronger. Say it was Ottinger. The Nash equilibrium outcome would then be for Ottinger's supporters to approve only Ottinger, for Goodell's supporters to approve both Goodell and Ottinger, and for Buckley's supporters to approve Buckley alone.

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The Road to Conscious Machines by Michael Wooldridge

Probably the most famous idea in game theory, and an idea that came to form the bedrock for decision-making in multi-agent systems, is that of Nash equilibrium. The idea of Nash equilibrium was formulated by John Forbes Nash Jr, whom we met earlier as someone invited to John McCarthy’s summer school on AI at Dartmouth College in 1956. He was jointly awarded the 1994 Nobel Prize in Economics (along with John Harsanyi and Richard Selten), for his work on Nash equilibrium. The basic idea of a Nash equilibrium is easy to understand. Suppose we have just two agents, each of whom has to make a choice. Suppose Agent One chooses to do x and Agent Two chooses to do y.

The idea is that their decisions will have been good ones (technically, they form a Nash equilibrium) if neither agent regrets their choice. That is: Agent One is satisfied that, given that Agent Two did y, doing x was the best thing for Agent One; and Agent Two is satisfied that, given that Agent One did x, doing y was the best thing for Agent Two. Nash equilibria are called equilibria because they capture a kind of stability in decision-making: neither agent has any incentive to do anything else. The multi-agent systems community rapidly adopted game theory ideas such as the Nash equilibrium as the basis for decision-making in their systems – but a now-familiar difficulty appeared.

MYCIN A classic expert system from the 1970s, which acted as a doctor’s assistant, diagnosing blood diseases in humans. narrow AI In contrast to General AI, this is the idea of building AI systems that focus on very specific problems, rather than trying to be capable of the full range of human intellectual abilities. The term is mainly used in the media: it isn’t really used in the AI community itself. Nash equilibrium A core concept in game theory, where a group of decision-makers are all simultaneously satisfied that they did the best they could, given the choices made by others. natural language understanding Programs that can interact in ordinary human languages like English. neural networks/neural nets An approach to machine learning using ‘artificial neurons’.

The Ethical Algorithm: The Science of Socially Aware Algorithm Design by Michael Kearns, Aaron Roth

A matching with this property is not at risk of unraveling as students and hospitals iteratively defect from their proposed matches. A stable matching is conceptually quite similar to a Nash equilibrium, but now two parties (a candidate and a medical school) must jointly defect to a mutually preferred outcome, due to the two-sided nature of the market. And like a Nash equilibrium, a stable matching in no way promises that everyone will be satisfied with the outcome: a candidate assigned to her 117th-favorite hospital may not be happy, but as in a Nash equilibrium, there is nothing she can do about it, because the 116 hospitals she prefers already have candidates they like better than her.

It is assumed that each “player” in the system (such as a user of Coffee Meets Bagel) will behave selfishly (for example, by setting or changing her dating preferences) to advance her own goals, in response to similarly selfish behavior by others, and without regard to the consequences for other players or the global outcome. An equilibrium is thus a kind of selfish standoff, in which all players are optimizing their own situation simultaneously, and no one can improve their situation by themselves. Technically speaking, the underlying mathematical notion of equilibrium we refer to here is known as a Nash equilibrium, named for the Nobel Prize–winning mathematician and economist John Forbes Nash, who proved that such equilibria always exist under very general conditions. We’ll shortly have reason to consider non-equilibrium solutions to game-theoretic interactions, as well as alternative notions of equilibrium that are more cooperative.

We mentioned briefly in that chapter that one solution to this problem involved an algorithm that simulated play between a Learner who would like to minimize error and a Regulator who continually confronts the Learner with subgroups suffering discrimination under the Learner’s current model. This is another example of simulated game play as design principle, with the Regulator taking the place of a backgammon program or a Generator. Here the Regulator’s goal (fairness) may be in conflict with the Learner’s (accuracy), and the outcome (which is actually a Nash equilibrium of a precisely defined game) will be a compromise of the two—as desired. Similarly, game-theoretic algorithm design has also proven useful in differential privacy. For example, while there may not be much motivation to generate fake cat pictures—we have plenty of the real thing—there is very good reason to generate realistic-looking but fake or synthetic medical records.

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Misbehaving: The Making of Behavioral Economics by Richard H. Thaler

As a result they will guess 22, so I will guess 15.” Of course, there is no convenient place to get off this train of thinking. Do you want to change your guess? Here is another question for you: What is the Nash equilibrium for this scenario? Named for John Nash, the subject of the popular book (and biopic) A Beautiful Mind, the Nash equilibrium in this game is a number that if everyone guessed it, no one would want to change their guess. And the only Nash equilibrium in this game is zero. To see why, suppose everyone guessed 3. Then the average guess would be 3 and you would want to guess two-thirds of that, or 2. But if everyone guessed 2 you would want to guess 1.33, and so forth.

, p. 158. 210 “Professional investment may be likened”: Ibid. 212 A Beautiful Mind: Nasar (1998). 212 commonly referred to as the “beauty contest”: Camerer (1997). 212 first studied experimentally by . . . Rosemarie Nagel: Nagel (1995). 212 zero was the Nash equilibrium: Researchers have explored various alternatives to Nash equilibrium. See, for example, Geanakoplos, Pearce, and Stachetti (1989), McKelvey and Palfrey (1995), Camerer, Ho, and Chong (2004), Eyster and Rabin (2005), Hoffmann et al. (2012), and Tirole (2014). 215 “In the long run, we are all dead”: Keynes (1923), ch. 2, p. 80.

The FT agreed, and British Airways offered up two business-class tickets from London to the U.S. as the prize. Based on what you know now, what would be your guess playing with this crowd? The winning guess was 13. The distribution of guesses is shown in figure 10. As you can see, many readers of the Financial Times were clever enough to figure out that zero was the Nash equilibrium for this game, but they were also clueless enough to think it would be the winning guess.# There were also quite a few people who guessed 1, allowing for the possibility that a few dullards might not fully “get it” and thus raise the average above zero.** FIGURE 10 Many first and second level thinkers guessed 33 and 22.

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Human Compatible: Artificial Intelligence and the Problem of Control by Stuart Russell

(See the notes for the complete analysis.24) The general criterion is very simple, however: Alice’s strategy is the best she can devise, assuming that Bob’s is fixed. Bob’s strategy is the best he can devise, assuming that Alice’s is fixed. If both conditions are satisfied, we say that the strategies are in equilibrium. This kind of equilibrium is called a Nash equilibrium in honor of John Nash, who, in 1950 at the age of twenty-two, proved that such an equilibrium exists for any number of agents with any rational preferences and no matter what the rules of the game might be. After several decades’ struggle with schizophrenia, Nash eventually recovered and was awarded the Nobel Memorial Prize in Economics for this work in 1994.

For Alice and Bob’s soccer game, there is only one equilibrium. In other cases, there may be several, so the concept of Nash equilibria, unlike that of expected-utility decisions, does not always lead to a unique recommendation for how to behave. Worse still, there are situations in which the Nash equilibrium seems to lead to highly undesirable outcomes. One such case is the famous prisoner’s dilemma, so named by Nash’s PhD adviser, Albert Tucker, in 1950.25 The game is an abstract model of those all-too-common real-world situations where mutual cooperation would be better for all concerned but people nonetheless choose mutual destruction.

Now, Alice reasons as follows: “If Bob is going to confess, then I should confess too (ten years is better than twenty); if he is going to refuse, then I should confess (going free is better than spending two years in prison); so either way, I should confess.” Bob reasons the same way. Thus, they both end up confessing to their crimes and serving ten years, even though by jointly refusing they could have served only two years. The problem is that joint refusal isn’t a Nash equilibrium, because each has an incentive to defect and go free by confessing. Note that Alice could have reasoned as follows: “Whatever reasoning I do, Bob will also do. So we’ll end up choosing the same thing. Since joint refusal is better than joint confession, we should refuse.” This form of reasoning acknowledges that, as rational agents, Alice and Bob will make choices that are correlated rather than independent.

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Rationality: What It Is, Why It Seems Scarce, Why It Matters by Steven Pinker

As he considers what Amanda might do, row by row, he has no reason to pick one of his moves over the other two, and will arrive at the same “mixed” strategy, playing each option with a probability of ⅓. If Brad were to deviate from this strategy, Amanda would change hers to exploit him, and vice versa. They are locked in a Nash equilibrium, named after the mathematician John Nash (the subject of the movie A Beautiful Mind ). Each is playing the best strategy given the opponent’s best strategy; any unilateral change would make them worse off. The discovery that in some situations a rational agent must be superhumanly random is just one of the conclusions from game theory that seems outlandish until you realize that the situations are not uncommon in life.

The mice are collectively worst off if none of them volunteers and best off if one of them does—which does not guarantee that they will arrive at this happy ending, since there’s no Head Mouse to draft one of them into possible martyrdom for the good of the horde. Rather, each mouse rolls the die because no mouse would do better by unilaterally switching to a different strategy. Here again they are in a Nash equilibrium, a standoff in in which all the players stick with their best choice in response to the others’ best choices. Rendezvous and Other Coordination Games A dog-eat-dog contest like Scissor-Paper-Rock and a nervous hypocritical standoff like the Volunteer’s Dilemma involve a degree of competition.

We play it when we drive or walk along a narrow path and face an oncoming traveler, requiring that someone yield, and when we engage in formal and informal bargaining. Public examples include foreclosing or defaulting on a debt, and brinkmanship standoffs in international relations like the Cuban Missile Crisis of 1962. Chicken has a Nash equilibrium in which each player takes some chance at standing his ground and otherwise swerves, though in real life this solution may be moot because the rules of the game may be enriched to include signaling and alterations to the strategy set. In chapter 2 we saw how a paradoxical advantage can go to a player who is visibly crazy or out of control, making his threats credible enough to coerce his opponent into conceding—though with the shadow of mutual destruction hanging over them if both go crazy or lose control simultaneously.12 Some games consist not of a one-shot encounter in which the players make a single move simultaneously and then show their hands, but a series of moves in which each responds to the other, with the payouts settled up at the end.

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Obliquity: Why Our Goals Are Best Achieved Indirectly by John Kay

IBM, relieved, called it quits.3 Even in chess, with a limited range of legal moves, the number of possible outcomes multiplies so rapidly that exhaustive calculation is beyond the scope of even the most powerful computer yet imagined. There is a formal procedure for describing such iterations called game theory, and its most basic solution concept—the Nash equilibrium—supposes that each player adopts the best strategy available if the other player does the same. We can expect that there is a Nash equilibrium solution to the game of chess, but we don’t know what it is. In every game of chess that has ever been played, there are moves for at least one of the players that are better than the one played. Or to be exact, we don’t know for sure that there aren’t.

Messner, Reinhold metaphors Microsoft military affairs military contracts milk Mill, John Stuart misers mission statements Mobutu Sese Seko monetary targets monocultures “moral algebra” Morita, Akio mortgages Moses, Robert motorcycles mountain climbing Mount Everest “muddling through” Munger, Charles Munich Agreement (1938) music nail factories Napoleon I, emperor of France Nash equilibrium National Park Service, U.S. natural selection Nazism negotiation Nettle, Daniel neural responses New Oxford Book of English Verse, The Newsweek New York, N.Y. Nigeria Nixon, Richard M. Nobel Prize normal distribution North Vietnam Northwest Passage Notre Dame cathedral Nozick, Robert Obama, Barack objectivity obliquity: adaptation in behavior and complexity inherent to eclecticism and flow and geographical happiness achieved by incompleteness and as indirect approach interactions for irrationality and linearity vs.

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Here Comes Everybody: The Power of Organizing Without Organizations by Clay Shirky

Assuming that the two people can’t communicate with each other and don’t trust each other (about which more in a moment), the worst outcome—number four—is the rational one, an outcome called a Nash equilibrium. The dilemma of the Prisoners’ Dilemma is that, because it is a one-off transaction in which you and I can’t communicate with each other, we can’t coordinate any outcome better than the dismal Nash equilibrium. (This is the same math underlying the Tragedy of the Commons, where the Nash equilibrium encourages individual defection, even as it damages the group.) Things change, though, when the prisoners interact with each other repeatedly, a version called an iterated Prisoners’ Dilemma.

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Against the Gods: The Remarkable Story of Risk by Peter L. Bernstein

Looking downward vertically, we find that both the choices rank higher than 4: the politicians would rather do nothing or run a deficit than follow a policy that cost them their jobs if their constituents lose their jobs as a result. This outcome is known as a Nash Equilibrium, named after John Nash, another Princetonian and one of the 1994 winners of the Nobel Prize for his contributions to game theory.18 Under the Nash Equilibrium the outcome, though stable, is less than optimal. Both sides would obviously prefer almost anything to this one. Yet they cannot reach a better bargain unless they drop their adversarial positions and work together on a common policy that would give each a supportive, or at least a neutral, role that would keep them from getting into each other's way.

In January 1995, the publication Pensions and Investments reported on another application of game theory in making investments. ANB Investment Management & Trust in Chicago had introduced a strategy explicitly designed to avoid the Winner's Curse. The chief investment officer, Neil Wright, saying he had based the strategy on the Nash Equilibrium, claimed that the Winner's Curse is usually associated with stocks that have abnormally wide price ranges, which "means there is a lot of uncertainty about how the company will do." A wide price range also indicates limited liquidity, which means that a relatively small volume of buying or selling will have a significant impact on the price of the stock.

XXIX, No. 2 (May), pp. 413-433. Leinweber, David J., and Robert D. Arnott, 1995. "Quantitative and Computational Innovation in Investment Management." Journal of Portfolio Management, Vol. 22, No. 1 (Winter), pp. 8-16. Leonard, Robert J., 1994. "Reading Cournot, Reading Nash: The Creation and Stabilisation of Nash Equilibrium." Economic Journal, Vol. 104, No. 424 (May), pp. 492-511. Leonard, Robert J., 1995. "From Parlor Games to Social Science: Von Neumann, Morgenstern, and the Creation of Game Theory." Journal of Economic Literature, Vol. XXXIII, No. 2 (June), pp. 730-761. Loomis, Carol J., 1995. "Cracking the Derivatives Case."

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The Secret of Our Success: How Culture Is Driving Human Evolution, Domesticating Our Species, and Making Us Smarter by Joseph Henrich

Thus, the predicted winning strategy in a contest of intelligent rational actors is that Matchers should randomize their responses, playing L 50% of the time, while Mismatchers should randomize by playing L only 20% of the time. This outcome is called the Nash equilibrium. The fraction of the time that one should play L can be moved around by simply changing the payoffs for matching or mismatching on L or R. A research team from Caltech and Kyoto University tested six chimpanzees and two groups of human adults: Japanese undergraduates and Africans from Bossou, in the Republic of Guinea. When chimpanzees played this asymmetric variant of Matching Pennies (figure 2.4), they zoomed right in on the predicted result, the Nash equilibrium. Humans, however, systematically and consistently missed the rational predictions, with Mismatchers performing particularly poorly.

Chimpanzees seem to be better at individual learning and strategic anticipation, at least in this game.20 The performance of the apes in this setup was no fluke. The Caltech-Kyoto team also ran two other versions of the game, each with different payoffs. In both versions, the chimps zeroed in on the Nash equilibrium as it moved around from game to game. This means that chimps can develop what game theorists call a mixed strategy, which requires them to randomize their behavior around a certain probability. Humans, however, often struggle with this. A final insight into the humans’ poor performance comes from an analysis of participants’ response times, which measures the time from the start of a round until the player selects his move.

The humans would also argue that Ayumu is clearly a ringer who figured out some secret way of winning that none of his fellow chimps have replicated. Humphrey (2012) provides an interesting discussion of potential issues with this research. 19. See Byrne and Whiten 1992, Dunbar 1998, and Humphrey 1976. 20. See Martin et al. 2014. The average deviation from the Nash equilibrium target was 0.02 for the chimps but 0.14 for the humans. 21. See Cook et al. 2012, Belot, Crawford, and Heyes 2013, and Naber, Pashkam, and Nakayama 2013. 22. On heuristics and biases from psychology and economics, see Gilovich, Griffin, and Kahneman 2002, Kahneman 2011, Kahneman, Slovic, and Tversky 1982, Camerer 1989, Gilovich, Vallone, and Tversky 1985, and Camerer 1995.

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A Mathematician Plays the Stock Market by John Allen Paulos

If the group continues to play this game, they will gradually learn to engage in ever more iterations of this meta-reasoning about others’ reasoning until they all reach the optimal response, which is 0. Since they all want to choose a number equal to 80 percent of the average, the only way they can all do this is by choosing 0, the only number equal to 80 percent of itself. (Choosing 0 leads to what is called the Nash equilibrium of this game. It results when individuals modify their actions until they can no longer benefit from changing them given what the others’ actions are.) The problem of guessing 80 percent of the average guess is a bit like Keynes’s description of the investors’ task. What makes it tricky is that anyone bright enough to cut to the heart of the problem and guess 0 right away is almost certain to be wrong, since different individuals will engage in different degrees of meta-reasoning about others’ reasoning.

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Never Let a Serious Crisis Go to Waste: How Neoliberalism Survived the Financial Meltdown by Philip Mirowski

If one cites the canonical Arrow-Debreu model of general equilibrium, then one can pair it with the Sonnenschein-Mantel-Debreu theorems, which point out that the general Arrow-Debreu model places hardly any restrictions at all on the functions that one deems “basic economics,” such as excess demand functions. Or, alternatively, if one lights on the Nash equilibrium in game theory, you can pair that with the so-called folk theorem, which states that under generic conditions, almost anything can qualify as a Nash equilibrium. Keeping with the wonderful paradoxes of “strategic behavior,” the Milgrom-Stokey “No Trade theorem” suggests that if everyone really were as suspicious and untrusting as the Nash theory makes out, then no one would engage in any market exchange whatsoever in a neoclassical world.

., “A Procurement Auction for Toxic Assets with Asymmetric Information,” p. 6. 132 Ausubel and Cramton, “Auctions for Injecting Bank Capital”; Klemperer, “The Product-Mix Auction”; Armantier et al., “A Procurement Auction”; Swagel, “The Financial Crisis”; Armantier et al., “A Procurement Auction.” 133 Ausubel and Cromtom, “Auctions for Injecting Bank Capital,” p. 4. More specifically, Ausubel et al. have since acknowledged, “there is no Bayesian Nash equilibrium bidding strategy for a similar auction that we can use as a benchmark. The reference price auction is beyond current theory” (“Common-Value Auctions with Liquidity Needs”). 134 Paulson, On the Brink, pp. 258, 264, 334, 363–68, 389; see also Swagel, “The Financial Crisis,” pp. 50–52, 58. 135 Ausubel and Cramton, “Auctions for Injecting Bank Capital.” 136 “Study Suggests Buying Toxic Assets Could Work,” NPR, November 18, 2008, available at www.npr.org/templates/story/story.php?

Index A Acemoglu, Daron Adbusters Admati, Anat AEA (American Economics Association), AEI (American Enterprise Institute) “After the Crash of 2008” (Prasch), The Age of Uncertainty (PBS series) Agnotology, defined Agriculture, Department of AIG Financial Products Akerlof, George Allais, Maurice AlphaSimplex American Economic Review American Economics Association (AEA) American Enterprise Institute (AEI) American Finance Association American Institute of Certified Public Accountants American Majority Americans for Prosperity Ameriquest Angelides, Phil Anglo Irish Bank Animal Spirits (Akerlof and Shiller) Annapolis Center AOL Armey, Dick Arnsperger, Christian Aron, Raymond Arrow–Debreu theory Arrow, Kenneth Artaud, Antonin, The Theatre and Its Double, Atlanta Federal Reserve Bank Atlas Economic Research Foundation Atlas Shrugged (Ayn Rand) Audacity of Intervention Auerbach, Robert Austrian School of economics Austrian-inflected Hayekian legal theory Austro-libertarianism Ausubel, Lawrence B Bailey, Martin Baker, Dean Bank concentration in US Bank of America Bank of New York Mellon Bank of Sweden Bank of Sweden Nobel Prize Barclays Barnett, Clive Barro, Robert Basel III Bayesian Nash equilibrium Bear Stearns Beck, Glenn Becker, Gary The Beginning of History (De Angelis) Behrent, Michael Benjamin, Walter Benson, Bruce Berliner Zeitung Bernal, J. D. Bernanke, Ben on asset purchase program Brunnermeier on as Chairman of Federal Reserve Bank Board on CRA on economic crisis as economic influence on EMH on Friedman on Great Moderation on Great Recession “hold-to-maturity” prices Kestenbaum on on Lehman failure Mirowski on on mortgage market on “Panic of 2007” paper pronounced absolution upon orthodox economics profession shadow banking on TARP testimony before FCIC Bernard, Andrew Bernstein, Jared Bertelsmann AG Besley, Tim Bhagwati, Jagdish Big Lie The Big Short (Lewis) The Birth of Biopolitics (Foucault) Black Rock Black-Scholes option pricing Blackstone Group Blackwater (Scahill) Blanchard, Olivier Blinder, Alan Bloomberg, Michael Bockman, Johanna, Markets in the Name of Socialism Body Alteration Boettke, Peter Bookstaber, Richard Bootle, Roger Born, Brooksley Boskin, Michael Bradley Foundation “Break the Glass: Bank Recapitalization Plan” (Swagel) Brenner, Robert Bretton Woods Bristol University British Academy British National Health Service British Royal Society Brookings Institution Brooks, David Brown, Gordon Brown, Wendy Brunnermeier, Markus Buchanan, James Buiter, Willem Bulow, Jeremy Bush, George Business Week Buycott C Calabria, Mark Caldwell, Bruce Calomiris, Charles Calvo, Guillermo Cambridge University Cameron, David Campbell, John Capitalism and Freedom (Friedman) Carbon emission permits Cassano, Joseph Cassidy, John Cato Institute CDS (Credit Default Swap) Center for Audit Quality Center for Market Processes at GMU Center for the Dissemination of Economic Information CETUSA (Council for Educational Travel in the USA) CFPB (Consumer Financial Protection Bureau) Change.org Chari, V.

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Culture and Prosperity: The Truth About Markets - Why Some Nations Are Rich but Most Remain Poor by John Kay

After making fundamental contributions to mathematics and quantum physics, he turned his attention briefly to economics, which he found "a million miles away from an advanced science." 20 Von Neumann became head of the U.S. Atomic Energy Commission-and the inspiration for Dr. Strangelove-before dying at the age of fifty-three. John Nash was author of the principal solution concept in game theory-the Nash equilibrium-but his productive career was ended by schizophrenia. His health partially restored, he was awarded the Nobel Prize in 1994. 21 Nash was played by Russell Crowe in an Oscar-winning film of his life, A Beautiful Mind. Institutional (or transactions cost) economics regards as its founder Ronald Coase,n a British economist who spent most of his career at the University of Chicago.

His colleague cries out in alarm, "Run, there is no time to waste." The economist smiles complacently. "Don't worry," he says, "the bear has to work it out too." The joke is not particularly funny, but it contains an important truth. 16 When economists adopted game theory, they assumed rational-self-regarding, materialist-behavior. In a Nash equilibrium, each player adopts the best strategy given the strategies of all other players. Biologists also adopted game theory, but did notcould not-assume their subjects had access to laptops. They developed the concept of an evolutionary stable strategy. 17 What behavior by bears would allow them to survive and thrive, even in the face of incursion by other bears with different behavior?

Supposedly devised by Merrill Glood and Melvin Dresher, the problem was posed in story form by Albert Tucker to explain his research to Stanford psychologists. 10. Marwell and Ames (1981). 11. The "folk theorem" of game theory (see, for example, Fudenberg and Tirole [1991], chapter 5), so called because its attribution is unclear, claims that all such strategies are Nash equilibrium in an indefinitely repeated game. We behave as we are expected to. 12. Axelrod (1984, 1997). 13. Basu (2000). 14. See Cronin (1991) for an explanation of these biological models. See Frank (1988) for a development of their economic analogues. Gintis (2000) describes both. 15. The classic statement of group selection arguments is Wynne-Edwards (1962), which helped provoke the decisive refutation by G.

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A Little History of Economics by Niall Kishtainy

He said that the outcome of a game – its ‘equilibrium’ – is that in which each player does the best for himself given what the other player does. When everyone’s doing that, no one has any reason to change what they’re doing, so that’s the equilibrium of the game. Nash proved that most games have an equilibrium – what became known as a ‘Nash equilibrium’. Take me and my enemy. Given that my enemy buys missiles, then my best response is to do the same: the worst thing would be to be unarmed in the face of enemy threats. The same reasoning applies to my enemy: if I arm, then they should definitely arm. Both of us building up our stock of missiles is the equilibrium of the game.

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The New Rules of War: Victory in the Age of Durable Disorder by Sean McFate

There may be a legitimate government in place, but it’s the deep state that really calls the shots. The institutions that comprise the deep state do not plot their actions like participants in a conspiracy. Rather, they engage in passive synchronization. They cooperate because their institutional interests align, as in a Nash equilibrium, resulting in mutually reinforcing actions that protect their common goals. Gradually this tacit consensus congeals into a deep state that can control a nation. They can overrule, sabotage, and reverse legitimate government decisions with no accountability or even visibility. Conspiracies and deep states are natural enemies.

(West Point), 235, 236 Military budget, 37–38, 41, 46, 47, 50, 102, 106–7, 445 Military contractors, 51, 101–2, 128–31 Military education, 235–40 Military force, declining utility of, 104–8 Military-industrial complex, 50, 166–67 Militias, 3, 101, 123–24, 153 Mimicry operations, 191 Mitchell, William “Billy,” 17–19, 20, 238, 249, 250 Mobutu Sese Seko, 157 Montgomery, Bernard, 234 Moral corruption, 113 “Moral hazard,” 186–87 More, Thomas, 127 Morocco, 97 Mueller, Robert, 202 Mutually assured destruction (“MAD”), 78–79 Myanmar, 150 My Lai massacre, 122 Myth-busting, 111 Myth of bifurcated victory, 232–33, 235 Napoleon Bonaparte, 32, 230, 250 Narco-wars. See Drug wars Narrative, controlling the, 41, 66, 67–68, 108–13, 227 Nash equilibrium, 161 Nasrallah, Hassan, 242 Natanz nuclear facility, 16 National debt, 46, 167 National Defense University, 23, 71, 232–33, 237–38 National guard vs. active duty, realignment of, 38–40 Nationalism, 105 National Security Agency, 137–38, 202 National Security Strategy, 75, 76–77 Nation-building, 4, 93–94, 150 Nation-states, 8, 247 conventional war and, 30–32 retreat of, 147–50 NATO (North Atlantic Treaty Organization), 2, 13, 21, 33, 37, 103–4, 168, 200, 245 Naval training, 55–57 Navy SEALs, 38, 172 Newbold, Gregory, 263n New Rules of War, 6, 9–10, 80, 248 New superpowers.

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The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation by Hannah Fry

The best-looking man should go for the blonde, while the other three should pair off with the brunettes. In that case, if any of the three tried to switch to the blonde at the last minute, their attempts would be rejected and only damage their chances with the brunettes. All the men would then be doing what’s right for themselves (this is called a ‘Nash equilibrium’), and at the same time doing what’s best for the group (making this also a ‘Pareto equilibrium’). Sadly, it’s rather rare to find such a neat real-world situation, with four opinion-free brunette clones and one stand-out blonde babe whom everyone is madly in love with. In real life, people have different preferences in a group, and generally it’s difficult to persuade people to ignore those preferences for the greater good.

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Global Inequality: A New Approach for the Age of Globalization by Branko Milanovic

The current era of globalization has witnessed a huge increase in available labor, both because world population has increased by two-thirds since 1980 and because China and the former communist countries have entered the global labor market. This growth in the availability of labor, according to Solow, has weakened labor’s position worldwide and allowed capital owners to take most of the rent for themselves. A similar idea is expressed by Chau and Kanbur (2013), who model it as a Nash equilibrium game where the fallback position of capital, because of its ability to move from one country to another in search of lower taxes, is much stronger than that of labor. The reasons for the increase in inequality in OECD countries have been extensively studied in the last two decades, since the increase became apparent.

See also specific countries Milanovic, Branko, 16, 18, 52, 121, 122, 253n3, 261n30 military-industrial complex, 163 military power, 250n33, 251nn40,41 Miller, David, 255n19 mobility, upward, 202–204, 261n32 Moellendorf, Darrel, 142 money, 14–15, 236, 239. See also rich people and money monopolization, 75 Moraga, Jesús Fernández-Huertas, 255n16 Morrisson, Christian, 119, 121, 253n2 Myrdal, Gunnar, 20–21 Nash equilibrium game, 106 nationalism, methodological, 235–239 nationalization, 100 national self-determination, 139–142 nativism, 164, 191, 204, 208, 210 Nefedov, Sergey, 247n17 Neiman, Brent, 181 neoliberalism, 20, 158 New Deal, 72, 98 “new Democrat” era, 54 “New Labour” era, 54 “new society,” 257n2 nineteenth century: late-twenty-first century compared, 5; Napoleonic wars and, 62, 80; markets and, 95; inequality among countries and, 119–120; global and US inequality, 124; horizontal inequality and, 225–226; inequality studies, 253n3.

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Infonomics: How to Monetize, Manage, and Measure Information as an Asset for Competitive Advantage by Douglas B. Laney

Absolutely. Indeed, many if not most microeconomic and macroeconomic principles can be applied to information assets. Some are obvious and need little treatment, such as the diminishing marginal cost of information (a feature of any storage device or service). Yet others like Ricardian Rent, Nash Equilibrium, and Bekenstein Bounds are out of bounds for a book of this nature. Therefore, we’ll explore only those which have the greatest relevance in the context of information assets, and that require some reformulation to guide information producers and consumers such as CDOs, CIOs, and enterprise-, application-, and data architects.

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Priceless: The Myth of Fair Value (And How to Take Advantage of It) by William Poundstone

Choices reveal all that we can know of utility, and utility in turn determines the prices that consumers are willing to pay. When someone is given a free choice between A and B, he simply consults his invisible price tags and chooses the one with the higher utility. Decision making is thus reduced to numbers. This assumption leads naturally to most of the standbys of economic theory, from demand curves to the Nash equilibrium. That brings us back to von Neumann’s contribution. Many economic choices are gambles. Given our uncertain world, the difficult and interesting choices are always gambles of one kind or another. It is therefore necessary to assign prices to gambles. According to von Neumann, the way to do this is to multiply each possible outcome’s subjective price by its probability, and total the results.

Reed, 3–4, 19–21 Morgenstern, Oskar, 50, 51, 54, 55 Mormons, 28 Morrissey, Paul, 202–203, 205 MRI scans, 168 MSNBC, 258 Mugabe, Robert, 223 Mullainathan, Sendhil, 146–47, 245, 246 Murphy, Charles B. G., 49, 71 Murray, Bill, 208–209 Mussweiler, Thomas, 90, 269–71 Nash equilibrium, 51 National Broadcasting Company (NBC), 255 National Economic Council, 262 National Football League (NFL), 156–66 National Geographic, 93 National Science Foundation, 122, 197 Nature Conservancy, 202 Nazis, 83–84 Neale, Margaret, 196–201, 203, 207, 208, 212 Negotiating Rationally (Bazerman and Neale), 212 negotiations, 116, 196, 211–12; anchoring in, 207–208, 211; business, 197; divorce, 234–36; fairness in, 105, 116; gender and, 236–38, 241–44; race and, 242–44; see also bargaining; ultimatum game Nestlé, 6 Netflix, 174–75 Netherlands, 130–33 Nettle, Daniel, 283 neuroeconomics, 249–50, 252 Nevada Gaming Commission, 72 Newcastle University, 282 Newsweek, 125–26 New York Giants football team, 166 New York Times, The, 185, 203, 227, 235, 236, 266 Nikon cameras, 145 99-cent stores, 184–85, 189, 190 Nobel Prize, 10, 11, 56, 57, 60, 83, 127 Nocera, Joseph, 236 Nokia, 6 NORAD, 52 Nordstrom’s department stores, 190 Norma’s restaurant (New York), 159 Northcraft, Gregory, 196–201, 203 Northwestern University, Kellogg Graduate School of Management, 218 Obama, Barack, 262 O’Dell, Brandon, 159, 161, 186 Oechssler, Jörg, 213–14 Olive Garden restaurant chain, 160 Onassis, Jacqueline, 202 “opportunity” price increases, 161 Oregon, University of, 62 Oregon Research Institute (ORI), 25–28, 49, 62, 68, 79, 87 Organizational Behavior and Human Decision Processes, 200, 210 Orma people, 122 outrage theory, 19, 276–79 Oxford University, 122, 126, 220 oxytocin, 252–54 packaging, changing size and shape of, 4–6 pain, 138–39; psychophysics of, 136 Palestine, British, 81, 83, 84 Palin, Michael, 134 Palmer, Arnold, 227 Pampers disposable diapers, 153–54 Papua New Guinea, 123 Parago, 177 Paraguay, 123 Parker Meridien Hotel (New York), 159 Parrish, Darrell, 241 Pastis restaurant (New York), 161–62 Pavlov, Ivan, 229 Pearson, Wayne, 72 Pennsylvania, University of, 237 Pepsico, 6 perceptual illusions, 36–37, 84–85 Peru, 121–22 Peters, Michael, 114 Pfeiffer, Tim, 269–71 Philosophical Enquiry into the Origin of Our Ideas on the Sublime and Beautiful (Burke), 101 phone bills, 172–73 physical attractiveness, effects on salaries and prices of, 239–40 Physical Impossibility of Death in the Mind of Someone Living, The (Hirst), 266 Picasso, Pablo, 116 pigeon drop con, 253 Pinker, Steve, 126 Plateau, Joseph-Antoine Ferdinand, 31–32, 40 Plautus, 109–10 Plott, Charles R., 78–80, 263 Pogo cartoon, 76 Poincaré, Henri, 57 Ponticello, John, 72, 73 Post, Thierry, 130–33 power curve, 32–33 Prada, 155, 158 preference reversals, 64–70, 72, 78–80, 87; experiments in, 72–75, 78–80, 90–91; rejection by economists of, 77–78 Prelec, Drazen, 9, 102, 135, 138, 194, 216, 256 price-to-earnings (P/E) ratio, 261, 263 priming, 91–94, 280–81, 284–86; see also anchoring Princeton University, 50, 165; Woodrow Wilson School, 10 Procter & Gamble Company, 6, 153 Producers, The (musical), 14–15 products, changing size and shape of, 5 Professional Pricing Society, 147 prospect theory, 97–103, 132, 147, 170, 172, 220 Prudential Real Estate, 219 Pruitt, D.

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Information: A Very Short Introduction by Luciano Floridi

This sort of equilibrium qualifies as a Pareto-suboptimal solution (named after the economist Vilfredo Pareto, 1848-1923) because there could be a feasible change (known as Pareto improvement) to a situation in which no player would be worse off and at least one player would be better off. Unlike the other three outcomes, the case in which both prisoners defect can also be described as a Nash equilibrium: it is the only outcome in which each player is doing the best he can, given the available information about the other player's actions. Nash equilibria are crucial features in game theory, as they represent situations in which no player's position can be improved by selecting any other available strategy while all the other players are also playing their best option and not changing their strategies.

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Competition Demystified by Bruce C. Greenwald

The two conditions work together; if no competitor has a motive to change its current course of action (stability of behavior), then no change will occur, confirming the stability of expectations. This concept of the likely outcome to a competitive situation is referred to in game theory as a “Nash equilibrium,” after its developer John Nash of A Beautiful Mind and Nobel Prize fame. In the Lowe’s–Home Depot example, imagine that the current outcome has Lowe’s at \$115 per basket, Home Depot at \$105 per basket (box C). If Lowe’s expects Home Depot to keep its price at \$105, Lowe’s can improve its position by lowering its price to match Home Depot.

Mountain Dew Movie studios See also Broadcasting industry MS-DOS Murdoch, Rupert Music industry, recorded cost structure of history iPod’s influence industry map market segments Nalco, Nash, John equilibrium theory developed by, linear invariance developed by, threat point outcomes developed by, Nash equilibrium NBC, competitors programming strength of Net present value. (NPV) Netscape Navigator Network effect benefits Networks (telecommunications). See also Broadcasting industry Cisco’s influence Research and development telecommunications New Deal Newman, Paul News Corporation Newton (Apple) New York Air Niche markets cooperation direct competition avoidance, efficiency growth dilemma identification Nifty Fifty Nintendo competitors decline economies of scale industry map licensing profitability quality retailers of technology Northwest Airlines Notebooks.

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Against Intellectual Monopoly by Michele Boldrin, David K. Levine

In the ensuing equilibrium, the total amount of investment is roughly the same as when no one was offering a subsidy, but everyone is now paying a distorting tax to finance the subsidy. When capital moves freely across countries, the very same logic applies to the international determination of IP rights. In what economists call the Nash equilibrium of this game, it is obvious that patent holders prefer to locate in countries with strong IP laws. This increases the stock of capital in the receiving country and reduces it everywhere else, especially in countries with low IP protection. Hence, absent international cooperation, there is a strong incentive for most countries to keep increasing patent protection, even in the absence of lobbying and bribing by intellectual monopolists.

., 197 establishment of by patents, 64 Lessig, Larry, 5 given to publicly funded research, 261 P1: KXF head margin: 1/2 gutter margin: 7/8 CUUS245-IND cuus245 978 0 521 87928 6 April 29, 2008 10:0 294 Index monopoly ( cont. ) taxes to recoup losses from piracy, government-enforced, 10, 64 119–120 granted by copyright and patents, 6 use of encryption, 34–35 impact on direction of R&D, 168 music piracy, 29, 32–33, 34, 119–120 model of, 169–170 muskets, 51 pressure for from early entrants, 48 and prevention of new entry, 69, Napster, 5, 89, 141–142. See also 93–94n.18 peer-to-peer networks and price discrimination, 70–71 Nash Equilibrium, 195 and progress, 9 National Committee on Plant Patents, 52 as reason for patenting, 76 NCSA Mosaic, 17 rent-seeking in, 68–69, 171, 234 New Growth Theory, 159–160 Schumpeterian view of, 169–171 news, distribution of on Internet, 26 and secrecy, 167–168 news industry Smith on, 10 attempts to gain monopoly in, 27–28 and social inefficiency, 69 copyright in, 27 Statute of Monopolies, 43–44 distribution of news on Internet, 26 and war, 82 newspapers, 29–30 monopoly, intellectual.

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Trend Following: How Great Traders Make Millions in Up or Down Markets by Michael W. Covel

Periods of high volatility are highly risky to traders. Such periods, however, can also present them with opportunities for great profits.9 252 Trend Following (Updated Edition): Learn to Make Millions in Up or Down Markets only way for everyone to succeed is to ignore the blonde and hit on the brunettes. The scene dramatizes the Nash Equilibrium, his most important contribution to game theory. Nash proved that in any competitive situation—war, chess, even picking up a date at a bar—if the participants are rational and they know that their opponents are rational, there is only one optimal strategy. That theory won Nash a Nobel Prize in economics and transformed the way we think about competition in both games and the real world.10 Building off Nash’s general thoughts, Ed Seykota lays out a basic risk definition from a trading perspective: “Risk is the possibility of loss.”

See also risk management Moneyball (Lewis), 181-182 Montana, Joe, 261 monthly newsletter of Dunn Capital Management, 42-43 Montier, James, 215 Morgan Stanley, 153 Motley Fool, 9 Mulvaney Capital Management, 136, 138 Mulvaney, Paul, 17, 124, 127, 172, 255, 259, 381-383 Munger, Charlie, 234 mutual fund industry, 296 NASDAQ, 3, 111, 233 Nash Equilibrium, 252 Nash, John, 251 National Institute of Standards and Technology, 225, 228-229 natural gas trading, 144-150 negative skew (statistics), 228 Neuro-Linguistic Programming (NLP), 201 The New Market Wizards (Schwager), 202, 300 New York Stock Exchange, 3 New York Yankees, 186, 188 Newton, Isaac, 238 Neyer, Robert, 188 Niederhoffer, Victor, 100, 164-168, 272, 289 Nightline (television program), 116 Nikkei 225 stock index, 131, 168-172, 238 Nin, Anais, 150, 273 NLP (Neuro-Linguistic Programming), 201 nonlinear versus linear world, 224-229 normal distributions, 226-227 numbers, trusting, 18 Oakland A’s, 185-186 objectivity and behavioral finance, 196 Occam’s razor, 212-213 Odean, Terrence, 212 Ostgaard, Stig, 126, 129 outcome versus process, 218-219 Oxford Dictionary, 213 The Oxford Guide to Financial Modeling (Ho and Lee), 125 panics.

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Data and Goliath: The Hidden Battles to Collect Your Data and Control Your World by Bruce Schneier

We have to weigh each of these benefits against the risks of the surveillance that enables them. The big question is this: how do we design systems that make use of our data collectively to benefit society as a whole, while at the same time protecting people individually? Or, to use a term from game theory, how do we find a “Nash equilibrium” for data collection: a balance that creates an optimal overall outcome, even while forgoing optimization of any single facet? This is it: this is the fundamental issue of the information age. We can solve it, but it will require careful thinking about the specific issues and moral analysis of how the different solutions affect our core values.

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Money: 5,000 Years of Debt and Power by Michel Aglietta

.), Beyond Microfoundations: Post-Walrasian Macroeconomics, Cambridge University Press, 1996, pp. 21–37. 13 Nobuhiro Kiyotaki and Randall Wright, ‘A Contribution to the Pure Theory of Money’, Journal of Economic Theory, vol. 53, no. 2, 1991, pp. 215–35. So-called search models belong to an evolutionist theory that proposes to demonstrate the possibility of decentralised exchanges. Indeed, the common acceptance of a form of money results from a bootstrap effect, as the result of a non-cooperative game. Money is the result of a Nash equilibrium. Just as there exist a multiplicity of such equilibriums, including a moneyless economy which thus has no exchanges (an autarchic equilibrium), there remains a fundamental indeterminacy over the means of exchange. 14 Michel Aglietta and André Orléan, La violence de la monnaie, Paris: PUF, 1982. 15 Michel Aglietta and Jean Cartelier, ‘Ordre monétaire des économies de marché’, in Michel Aglietta and André Orléan (eds), La monnaie souveraine, Paris: Odile Jacob, 1998, p. 131. 16 Orléan, L’Empire de la valeur, pp. 148–52. 17 Michel Aglietta, Pepita Ould Ahmed and Jean-François Ponsot, ‘La monnaie, la valeur et la règle’, Revue de la régulation, vol. 16, no. 2, Autumn 2014. 18 On the ontogenesis of money, see Aglietta and Orléan, La violence de la monnaie. 19 Albert O.

See also specific types of money absolute liquidity as essential quality sought for in, 37 alternative views of genesis of, 40t ambivalence of, 53–4, 61, 95, 138, 195 as common good, 80b creation of bank money, 44t as defined by three functions, 35 definition, 12, 32–3 essential function of, 33 as foundation of value, 17–58 as instituting relationship of social belonging, 79b as instituting value, 32 as institution of social belonging, 30–5 as intergenerational bond that guarantees immortality of society, 63 as language, 31–3, 78b, 82–3, 168 legitimacy of, 69–75 logical genesis of, 35–9 logic of in decadent Roman Republic, 102–3 making metal into, 43t as market’s logical foundation, 30 as more fundamental social bond than the market, 30 nationalisation of, 150 neutrality of, 27–30 new forms of, 164–83 as not integrated into pure economics, 28 as preceding market relations, 30 presence of as obsession, 26 problem of coordination of market exchange without, 19–22 as a relation of social belonging, 11–16 relationship of with finance, 12 as result of Nash equilibrium, 29n13 as sources of confidence in democratic societies, 75f and sovereignty, 83 studies of, 111, 112t as system, 83 teaching money, 75–80b as total social phenomenon, 81 value of, 29 as vulnerable to crises, 54 money anchorage regimes, 256t money market funds, 268, 273, 275, 385 money-neutrality hypothesis, 262, 267 Morgan, John P., 217, 219 Morgan, Lewis Henry, 67 Morgenthau, Henry, Jr, 316 multi-currency payment systems, 152, 153 Mundell, Robert, 349, 351–5 Mundell’s triangle, 352, 353, 354f Muth, John, 26 N NAIRU (non-accelerating inflation rate of unemployment), 268 National Bank Act of 1863, 140, 215, 216, 218 national currency, 69, 78b, 150, 188, 201, 222, 232, 236, 241, 314, 343, 362 national debt, 133–4, 203, 207 national financiers, 200 National Monetary Commission, 219 national payment systems, 143, 151 National Reserve Association, 220 nation-states, 122, 145–6, 147, 167, 200–1, 209, 287, 359 natural interest rate, 262, 267, 276, 278f, 280, 342 naturalist theory of utility value, 30, 53 naturalist theory of value, 31, 34, 36, 44, 64, 81 natural monetary order, 124 natural order, 4, 82, 125, 126, 128, 134, 145, 147, 162, 254, 296 natural rate, 262, 263, 264b, 278–9, 280, 281 neutral real interest rate, 267, 342 neutral real rate, 262, 263f, 267 New York Clearing House Association (NYCHA), 141, 219 Nixon, Richard, 326, 327 nominal natural rate, 279, 280 nominal rate, zero-limit to, 278–80 non-accelerating inflation rate of unemployment (NAIRU), 268 Nye, Joseph, 358n9 O objective financial asset prices, hypothesis of, 24n6 OECD, 279, 358, 391 official foreign exchange reserves, annual mean variation in, 321t order of Christendom, 125 ordoliberalism, 56, 96, 129, 130, 131, 149, 160, 161t, 254, 260–1, 366 Oresmes, Nicolas, 113 Organisation for European Economic Co-operation (OEEC), 319 Ossola report, 325 Overend Gurney Company, 211 overlapping generation models, 62, 63, 64, 66 overlapping hierarchical sovereignty, 105–6 P paeleomonies, 77b PAI (Immediate Action Programme), 234 Panic of 1907, 143 Panizza, Ugo, 343 paper money, 77b, 171, 206, 215 Patinkin, Don, 28 payments definition, 31–2 finality of, 34, 44–9, 53, 175, 350, 398 hierarchical organisation of, 52f large-value payments, 152–3, 155 low-value (retail) payments, 152 matrix of, 46t retail payments, 151, 154t as social judgement, 34–5 payments technology, 116, 138, 149, 175, 246 payment system(s), 34, 38, 39, 40–1, 42, 43, 44, 47, 49, 50, 51, 53, 54, 58, 61, 65, 69, 75, 78b, 79b, 80b, 83, 87–8, 100, 135, 136, 138, 141, 142, 143, 144, 150, 151, 185–6, 188t, 189, 195, 213, 220, 245–6, 247, 248, 249, 286, 290, 294, 313, 363, 398, 399.

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Strategy: A History by Lawrence Freedman

It states neither how people do behave nor how they should behave in an absolute sense, but how they should behave if they wish to achieve certain ends.”3 Their injunction was ignored and game theory came to be adopted as more of a descriptive than normative tool. One reason for this was the development of the Nash equilibrium, named after the mathematician John Nash (whose struggle with mental illness became the subject of a book and a movie).4 This was an approach to nonzero-sum games. The idea was to find a point of equilibrium, comparable to those in physics when forces balance one another. In this case, players sought the optimum way to reach their goals.

From the start, and to the frustration of the experimenters, the games showed individuals making apparently suboptimal choices. A person (the proposer) was given a sum of money and then chose what proportion another (the responder) should get. The responder could accept or refuse the offer. If the offer was refused, both got nothing. A Nash equilibrium based on rational self-interest would suggest that the proposer should make a small offer, which the responder should accept. In practice, notions of fairness intervened. Responders regularly refused to accept anything less than a third, while most proposers were inclined to offer something close to half, anticipating that the other party would expect fairness.17 Faced with this unexpected finding, researchers at first wondered if there was something wrong with the experiments, such as whether there had been insufficient time to think through the options.

Duncan Luce and Howard Raiffa, Games and Decisions: Introduction and Critical Survey (New York: John Wiley & Sons, 1957), 10. 3. Ibid., 18. 4. Sylvia Nasar, A Beautiful Mind (New York: Simon & Schuster, 1988). 5. John F. Nash, Jr., Essays on Game Theory, with an introduction by K. Binmore (Cheltenham, UK: Edward Elgar, 1996). 6. Roger B. Myerson, “Nash Equilibrium and the History of Economic Theory,” Journal of Economic Literature 37 (1999): 1067. 7. Mirowski, Machine Dreams, 369. 8. Richard Zeckhauser, “Distinguished Fellow: Reflections on Thomas Schelling,” The Journal of Economic Perspectives 3, no. 2 (Spring 1989): 159. 9. Milton Friedman, Price Theory: A Provisional Text, revised edn.

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The Inner Lives of Markets: How People Shape Them—And They Shape Us by Tim Sullivan

The year 1951 had seen a major technical advance that made proof of existence far easier than Wald might have realized. John Nash, the game theorist made famous by the book and movie A Beautiful Mind, had borrowed the fixed-point theorem of Japanese mathematician Shizuo Kakutani to prove the existence of Nash equilibrium in game theory. In Arrow’s retelling, at that point it was obvious how to go about proving the existence of competitive equilibrium, and it was a race among himself, French economist Debreu, and several others to see who could do it first and do it best. As Arrow recalls, he summarized his first attempt at proving the existence theorem in a working paper just before heading to Europe to give some lectures.

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How Many Friends Does One Person Need? Dunbar’s Number and Other Evolutionary Quirks by Robin Dunbar, Robin Ian MacDonald Dunbar

We also know that these risks are associated with your birth weight, which is itself partly a reflection of your experience in the womb. We also know that low birth weight affects childhood academic abilities, and IQ more generally. The intelligent butterfly The film A Beautiful Mind paid tribute to the genius, if also the troubled mind, of John Nash, discoverer of the Nash Equilibrium in mathematics and winner of the 1994 Nobel Prize for Economics. But what the headlines don’t tell us is whether behind the beautiful mind there was also a beautiful body – and not just that of Russell Crowe who played Nash in the film. In fact, it has always seemed to me that not all the swots I knew at school and university were dull, ugly or uncoordinated.

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More Than You Know: Finding Financial Wisdom in Unconventional Places (Updated and Expanded) by Michael J. Mauboussin

Eventually, the British, French, and German high commands undermined the live-and-let-live system by forcing raids, undermining the stability necessary to support the tacit agreements. 6 “Stern Stewart EVA Roundtable,” Journal of Applied Corporate Finance 7, no. 2 (Summer 1994): 46-70. 7 For an excellent discussion, see William Poundstone, Prisoner’s Dilemma (New York: Anchor Books, 1992). 8 The choice to add capacity gets both companies to the Nash equilibrium. 9 Axelrod, The Evolution of Cooperation, 27-54. 10 David Besanko, David Dranove, and Mark Shanley, Economics of Strategy, 2nd ed. (New York: John Wiley & Sons, 2000), 289-90. 11 Ibid., 293-302. 12 Adam M. Brandenburger and Barry J. Nalebuff, Co-opetition (New York: Currency, 1996), 120-22. 27.

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Life as a Passenger: How Driverless Cars Will Change the World by David Kerrigan

The presence of just a few autonomous vehicles can eliminate the stop-and-go driving of the human drivers in traffic, along with the accident risk and fuel inefficiency it causes, according to research from the University of Illinois.[39] Their experiments show that with as few as 5 percent of vehicles being automated and carefully controlled, it can eliminate stop-and-go waves caused by human driving behavior. Many people think that they can outwit others and improve their lot in a congested environment by making changes to their route. However, applying the Nash Equilibrium from Game Theory, (no one player can make himself better off by his own action alone), one person cannot solve congestion. In fact, individual attempts to circumvent congestion can have the opposite to the intended outcome - this is known as Selfish Routing - each person is moving through the network in the way that seems best to them, but everyone’s total behaviour may be the least efficient for the traffic network.

The Golden Ratio: The Story of Phi, the World's Most Astonishing Number by Mario Livio

And the most astonishing of all: Why are the laws of physics themselves expressible as mathematical equations in the first place? But this is not all. Mathematician John Forbes Nash (now world famous as the subject of the book and film biography A Beautiful Mind), for example, shared the 1994 Nobel Prize in economics because his mathematical dissertation (written at age twenty-one!) outlining his “Nash Equilibrium” for strategic noncooperative games inaugurated a revolution in fields as diverse as economics, evolutionary biology, and political science. What is it that makes mathematics work so well? The recognition of the extraordinary “effectiveness” of mathematics even made it into a hysterically funny passage in Samuel Beckett's novel Molloy, about which I have a personal story.

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A World Without Email: Reimagining Work in an Age of Communication Overload by Cal Newport

Similar scenarios of individual interest leading to collective hardship turn out to be common in many different settings—from unstable ecologies, to resource mining, to the behaviors surrounding shared refrigerators. Using the mathematical tools introduced in the mid-twentieth century by John Nash (of A Beautiful Mind fame), you can even precisely analyze this situation, which turns out to be a nice example of what game theorists would call an “inefficient Nash equilibrium.” This economic trivia informs our discussions here because when the hyperactive hive mind emerged due to the drivers summarized earlier in this chapter, communication in the modern office became yet another example of Lloyd’s thought experiment in action. Once your organization has fallen into the hive mind, it’s in each individual’s immediate interest to stick with this workflow, even if it leads to a bad long-term outcome for the organization as a whole.

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Superforecasting: The Art and Science of Prediction by Philip Tetlock, Dan Gardner

Because the contestants are aware of each other, and aware that they are aware, the number is going to keep shrinking until it hits the point where it can no longer shrink. That point is 0. So that’s my final answer. And I will surely win. My logic is airtight. And I happen to be one of those highly educated people who is familiar with game theory, so I know 0 is called the Nash equilibrium solution. QED. The only question is who will come with me to London. Guess what? I’m wrong. In the actual contest, some people did guess 0, but not many, and 0 was not the right answer. It wasn’t even close to right. The average guess of all the contestants was 18.91, so the winning guess was 13.

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The Myth of Capitalism: Monopolies and the Death of Competition by Jonathan Tepper

The optimal strategy is for the group to cooperate—no one talks to the blonde and they all talk to the less attractive friends. Nash's key idea was that among different players, they might all choose tacit cooperation rather than face competition. The solution to the problem of competition is called “Nash Equilibrium.” Nash didn't create game theory, but he developed it. His idea was a direct descendant of John von Neumann's Minimax theory. The idea is that players of a game won't seek to achieve the highest payout but will try to minimize their maximum loss. The easiest way to understand this is the example of a mother who allows her two children to divide a cake.

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Darwin Among the Machines by George Dyson

“The initial reaction of the economists to this work was one of great reserve, but the military scientists were quick to sense its possibilities in their field,” wrote J. D. Williams in The Compleat Strategyst, a RAND Corporation best-seller that made game theory accessible through examples drawn from everyday life.6 The economists gradually followed. When John Nash was awarded a Nobel Prize for the Nash equilibrium in 1994, he became the seventh Nobel laureate in economics whose work was influenced directly by von Neumann’s ideas. Nash and von Neumann had collaborated at RAND. In 1954, Nash authored a short report on the future of digital computers, in which the von Neumann influence was especially pronounced.

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The Age of Em: Work, Love and Life When Robots Rule the Earth by Robin Hanson

The existence of thousands or millions of copies of a team give those team copies many ways to learn from statistics about events in other teams. This makes it easier to score the performance of each team and member, via comparisons with other teams and members. This also tends to push em team behavior to more closely approximate an informed game theoretic Nash equilibrium, that is, a matched set of strategic behaviors that are less influenced by hidden information regarding the types of participants and the consequences of their actions. Statistics about other copies of a team make it harder for team members to deceive themselves about their past performance or their chances for future performance.

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The Precipice: Existential Risk and the Future of Humanity by Toby Ord

For example, consider the tension between what is best for each and what is best for all. This is studied in the field of game theory through “games” like the prisoner’s dilemma and the tragedy of the commons, where each individual’s incentives push them toward producing a collectively terrible outcome. The Nash equilibrium (the outcome we reach if we follow individual incentives) may be much worse for everyone than some other outcome we could have achieved if we had overcome these local incentives. The most famous example is environmental degradation, such as pollution. Because most of the costs of pollution aren’t borne by the person who causes it, we can end up in a situation where it is in the self-interest of each person to keep engaging in such activities, despite this making us all worse off.

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Radical Uncertainty: Decision-Making for an Unknowable Future by Mervyn King, John Kay

They find not the best move, but a move that is good enough. There is, in principle, a ‘best’ way of playing chess – a perfect game in which no move by either white or black could be improved on. This would be the ‘solution’ to the game of chess (which economists in characteristic style describe as the subgame perfect Nash equilibrium). But we do not have, and perhaps never will have, computers powerful enough to find that game. 41 If neither Magnus Carlsen (in 2019 the world champion) nor Deep Blue can play a perfect game of chess, it stretches the imagination to suppose that ordinary people and businesses could optimise the game of economic life.

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Traffic: Why We Drive the Way We Do (And What It Says About Us) by Tom Vanderbilt

From the point of view of the individual driver, this behavior makes sense. After all, if the driver gets off the highway and goes to Sure Thing Street, he or she will not save time. The driver will save time only if others get off the highway—but why should they? The drivers are locked into what is called a Nash equilibrium, a strategic concept from the annals of Cold War thinking. Popularized by the Nobel mathematician John Nash, it describes a state in which no one player of an experimental game can make himself better off by his own action alone. If you cannot improve your situation, why move to a different road?

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Superintelligence: Paths, Dangers, Strategies by Nick Bostrom

The team with the highest performance builds the first AI. The riskiness of that AI is determined by how much its creators invested in safety. In the worst-case scenario, all teams have equal levels of capability. The winner is then determined exclusively by investment in safety: the team that took the fewest safety precautions wins. The Nash equilibrium for this game is for every team to spend nothing on safety. In the real world, such a situation might arise via a risk ratchet: some team, fearful of falling behind, increments its risk-taking to catch up with its competitors—who respond in kind, until the maximum level of risk is reached. Capability versus risk The situation changes when there are variations in capability.

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Addiction by Design: Machine Gambling in Las Vegas by Natasha Dow Schüll

Along similar lines, Frederic Jameson has written of America that “no society has ever been quite so addictive, quite so inseparable from the condition of addictiveness as this one, which did not invent gambling, to be sure, but which did invent compulsive consumption” (2004, 52). 9. The concept of equilibrium as Rocky uses it here evokes a diverse set of expert meanings, from thermodynamics in physics, to economic concepts like the Nash equilibrium, to cybernetic theories of control and regulation, to ecological notions of systemic balance, to psychoanalytic understandings of how the pleasure principle and the death drive work to extinguish excitation and restore a state of rest (Freud 1961 [1920]; Bateson 1972). Although the state of equilibrium would seem at first glance to be contrary to the condition of addiction (which is associated with excess), in fact it plays a critical role in the addictive process (see chapter 4). 10.

Theory of Games and Economic Behavior: 60th Anniversary Commemorative Edition (Princeton Classic Editions) by John von Neumann, Oskar Morgenstern

The playing of games is dependent on abilities that game theory does not capture well, such as memory, the ability to process information and the quality of associations. The assimilation of these concepts constitutes one of the main challenges for the future. Will we see a new concept added to those of competitive equilibrium and Nash equilibrium as an additional pillar of economic thought? Finally, I can not help noticing that the book was written during the Second World War and published in 1944, a year of loss and tragedy. This coincidence and the role later played by certain institutions (which had been involved in security matters) in the development of game theory led some people to the ridiculous conclusion that “game theory is a plot.”

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Rationality: From AI to Zombies by Eliezer Yudkowsky

Because in advance of the lottery, this is the general policy that gives us the highest expectation of survival. . . . like I said: Real wars = not fun, losing wars = less fun. Let’s be clear, by the way, that I’m not endorsing the draft as practiced nowadays. Those drafts are not collective attempts by a populace to move from a Nash equilibrium to a Pareto optimum. Drafts are a tool of kings playing games in need of toy soldiers. The Vietnam draftees who fled to Canada, I hold to have been in the right. But a society that considers itself too smart for kings does not have to be too smart to survive. Even if the Barbarian hordes are invading, and the Barbarians do practice the draft.