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This book attempts to create an evolutionary theory of fairness. Sharing food is commonplace in the animal kingdom because it insures animals that share against hunger. Anthropologists report that hunter-gatherer societies which survived into the 20th century shared on a very egalitarian basis. What can such information tell us about the sense of fairness with which modern man is born? Using game theory as a basic tool, the book argues that fairness norms should be seen as a device for selecting an efficient equilibrium in the human game of life. Evolutionary arguments are then used to argue that the deep structure of this device resembles the original position formulated by John Rawls in his Theory of Justice. Such an evolutionary framework allows problems over welfare comparison and norm enforcement to be tackled in a manner that resolves the long debate between utilitarianism and egalitarianism.

Metaphysical moral theories can be loosely be divided into theories of the Good or Right. Naturalistic theories can be said to be theories of the seemly — what is appropriate in a particular place and time. This chapter explains how rights and duties can fit within a theory of the seemly. You have a right to do something if you do not have a duty not to do it. You have a duty to do something if you would otherwise diverge from equilibrium play in the social contract currently operated by your society.

The folk theorem shows that cooperative behavior can be sustained as a Nash equilibrium in indefinitely repeated games — a phenomenon known as reciprocal altruism. The same theorem offers a solution to various other social mysteries. Who guards the guardians? How are authority, blame, courtesy, dignity, envy, friendship, guilt, honor, integrity, justice, loyalty, modesty, ownership, pride, reputation, status, trust, virtue, and the like to be explained as emergent phenomena? How do beliefs that many people privately know to be false survive?

This chapter reviews the calumnies that are commonly directed at moral naturalists. Philosophical rationalism is compared unfavorably with the empirical tradition by drawing attention to the inadequacies in the reasoning that supposedly leads to Kant's categorical imperative. Moral naturalism is defended on the same basis as biological naturalism. Moral relativism — the big no-no for metaphysical moralists — is defended against a variety of common criticisms; reductionism gets the same treatment. Finally, the life of David Hume is advanced as a counter-example to those who feel that naturalism is necessarily dehumanizing or dispiriting.

This chapter looks to the broad consequences of the theory of fairness advanced in this book to questions of social reform. The traditional spectrum of political attitudes that ranges from the utilitarian left to the libertarian right is rejected in favor of a more realistic opposition between the neofeudal societies in which we currently live, and the prospect of fairer and freer societies that could be created by a planned program of decentralization which is identified with the whiggery that inspired the Glorious Revolution of 1688 and the Declaration of Independence of 1776. The contribution that game theory can make to such a program is briefly reviewed along with the deficiencies of the current theory.

If some external enforcement agency compels us to honor deals reached in the original position, then Harsanyi has shown that the outcome will be utilitarian. Under the same hypotheses, Rawls claims that the outcome will be egalitarian. This chapter confirms that Harsanyi is correct. It goes on to use the concept of an empathy equilibrium to predict the standard of interpersonal comparison needed to operate a utilitarian norm that will evolve in the medium run.

This chapter presents an overview of the book. It argues that the metaphysical approach to ethics is a failure and that the time has come to take a scientific view of morality. A social contract is taken to be the set of common understandings that allow the citizens of a society to coordinate. Such social contracts are seen as the product of biological and cultural evolution. To survive, a social contract must therefore be an equilibrium in the repeated game of life played by a society. Since the folk theorem of repeated game theory says that there are large numbers of such equilibria, fairness norms then become explicable as an equilibrium selection device that selects one of the many efficient equilibria of a society's game of life. It is suggested that the deep structure of such fairness norms is captured by John Rawls' notion of the original position, and is therefore universal in the human species. On the other hand, the standard of interpersonal comparison needed as an input to the original position is culturally determined.

Among other things, Baumard et al.'s “A Mutualistic Approach to Morality” considers the enforcement and establishment of moral norms, the interpersonal comparison of welfare, and the structure of fairness norms. This commentary draws attention to the relevance of the game theory literature to the first and second topic, and the social psychology literature to the third topic.

This note argues that the rationality of backward induction necessarily involves the study of counterfactuals.

Theories of focal points typically assume that games are accompanied by labelings or “frames” that relate the actions in the game to the environment in which the game is played. Attention then focuses on how players can exploit framing information to identify focal equilibria. This paper asks instead how evolutionary considerations determine which aspects of the environment are likely to be monitored by the players and hence appear as part of the framing information. Efficient monitoring turns out to be an unlikely outcome.

This paper examines evolutionary equilibrium selection in bargaining models. We show that random best-response and continuous best-response learning dynamics give rise to (different) simple sufficient conditions for identifying outcomes as stochastically stable. This allows us to characterize the implications of these dynamics in simple bargaining games.

This paper reviews the part played by economists in organizing the British third-generation mobile-phone licence auction that concluded on 27 April 2000. It raised 22.5 billion pounds ($34 billion or 2.5% of GNP) and was widely described at the time as the biggest auction ever. We discuss the merits of auctions versus "beauty contests", the aims of the auction, the problems we faced, the auction designs we considered, and the mistakes that were made.

This paper reports experiments with one-stage and two-stage alternating-offers bargaining games. Payoff-interdependent preferences have been suggested as an explanation for experimental results that are commonly inconsistent with players' maximizing their monetary payoffs and performing backward induction calculations. We examine whether, given payoff-interdependent preferences, players respect backward induction. To do this, we break backward induction into its components, subgame consistency and truncation consistency. We examine each by comparing the outcomes of two-stage bargaining games with one-stage games with varying rejection payoffs. We find and characterize systematic violations of both subgame and truncation consistency. Journal of Economic Literature Classification Numbers: C70, C78.

This paper reviews the part played by economists in organizing the British third-generation mobile-phone licence auction that concluded on 27 April 2000. It raised 22.5 billion pounds ($34 billion or 2.5 % of GNP) and was widely described at the time as the biggest auction ever. We discuss the merits of auctions versus 'beauty contests', the aims of the auction, the problems we faced, the auction designs we considered, and the mistakes that were made.

Selten (1980, J. theor. Biol.84, 93(N)/01) has shown that mixed strategies cannot be evolutionarily stable in asymmetric games. Because every interaction features some asymmetry, this result apparently precludes mixed strategies in an evolutionary setting. In Maynard Smith's Hawk–Dove game (1982, Evolution and the theory of games (UP-Cambridge), for example, Selten's result restricts attention to pure-strategy evolutionarily stable outcomes in which the animals use the ability to condition their actions on asymmetries to coordinate, with one playing Hawk and one playing Dove, and with conflicts in which both animals play Hawk never arising. This result contrasts with the intuition that the mixed equilibrium of the Hawk–Dove game captures important aspects of many animal interactions, including the possibility of conflict. In this paper, we follow Eshel and Sansone (1995, J. theor. Biol. 177, 341–356) in enriching Selten's model to incorporate an important aspect of animal interactions, namely that payoffs and asymmetries may both be imperfectly observed. In the richer model, we find conditions under which effectively mixed strategies are stable in asymmetric games, as well as conditions under which they are not stable. Behavior will be conditioned on asymmetries, leading to pure-strategy equilibria in which conflict is avoided, when there are relatively large, observable asymmetries and small observable variations in payoffs. Under opposite conditions, evolutionarily stable equilibria will appear that are effectively mixed, including the potential for conflict.

Our paper “Experimental Economics: Where Next?” contains a case study of Ernst Fehr and Klaus Schmidt’s work in which it is shown that the claims they make for the theory of inequity aversion are not supported by their data. The current issue of JEBO contains two replies, one from Fehr and Schmidt themselves, and the other from Catherine Eckel and Herb Gintis. Neither reply challenges any claims we make about matters of fact in our critique of Fehr and Schmidt on inequity aversion, although it is clear that if they could have refuted any single factual sentence then they would have done so. Both replies therefore implicitly concede that the facts quoted in our case study are correct. All the other issues raised in the two replies are just so much dust kicked up to distract attention from the only question that matters: Is it scientific to proceed like Fehr and Schmidt or is it not? Fehr and Schmidt say yes. So do Eckel and Gintis. The implications are quite far-reaching for those like us who think it is obvious that the answer is no. What other claims asserted by the school of Gintis et al can we trust? For example, Gintis makes the theory of inequity aversion one of the twin pillars of laboratory wisdom in his forthcoming book, The Bounds of Reason (Gintis, 2009, Chapter 3). He is even more fulsome when addressing sociologists in a joint paper with Fehr (Fehr and Gintis 2007, page 60)

There has been much discussion of the relative merits of selling government bonds using a uniform-price auction rather than the traditional discriminatory-price auction. Arguments in favor of the former have won the day in respect of the newly instituted auctions of index-linked bonds in the USA and UK. This short paper assesses the evidence and concludes that the advantages of uniform-price auctions have been oversold.

This paper characterizes modified evolutionarily stable strategies ( mess es) in Rubinstein's alternating-offers, infinite-horizon bargaining game. We show that a mess causes agreement to be achieved immediately, with neither player willing to delay the agreement by one period in order to achieve the other player's share of the surplus. Each player's share of the surplus is then bounded between the shares received by the two players in the unique subgame-perfect equilibrium of Rubinstein's game. As the probability of a break-down in negotiations becomes small (or discount factors become large), these bounds collapse on the subgame-perfect equilibrium.Journal of Economic LiteratureClassification Numbers C70, C78.

If the players in an alternating-offers bargaining game are averse to delays in reaching an agreement, then a unique subgame-perfect equilibrium exists. But the rationality requirements of the subgame-perfect equilibrium concept are too severe for this celebrated result of Ariel Rubinstein [21] to be relevant to the design of automated agents capable of negotiating on behalf of their clients. This paper therefore studies the play of bargaining games with alternating offers by finite automata.

The Paradox of the Absent-Minded Driver is used in the literature to draw attention to the inadequacy of Savage’s theory of subjective probability when its underlying epistomological assumptions fail to be satisfied. This note suggests that the paradox is less telling when the uncertainties involved admit an objective interpretation as frequencies. Ce que j’ai appris, je ne le sais plus. Le peu que je sais encore, je l’ai devine. Chamfort, Maximes et Pensees, 1975

A large part of economics, and economic theory in particular, relies on such solution concepts as Nash equilibrium and its refinements. Unfortunately, it is difficult to provide a solid theoretical or empirical justification for Nash equilibrium behaviour. ‘Rationality’, or even ‘common knowledge of rationality’, is not enough to generate such behaviour. Among other things, one also needs to assume that the players coordinate their beliefs about each other’s actions (Armbruster and Boege, 1979; Johansen, 1982; Bernheim, 1984; Pearce, 1984; Bernheim, 1986; Binmore, 1987; Aumann, 1987; Tan and Werlang, 1988; Aumann and Brandenburger, 1991). Moreover, in games with a dynamic structure, the very notion of rationality becomes problematic, and common knowledge of rationality may even lead to logical contradictions (Rosenthal, 1981; Binmore, 1987; Bicchieri, 1989; Basu, 1988, 1990).

My mother, like most mothers, was fond of the question: Suppose everybody behaved liked that? Her logic was the same as Spinoza’s (1674) in the quotation from his Tractatus Politicus that heads this chapter. Since things would be bad for everybody if everybody behaved selfishly, selfishness must therefore be irrational. Rousseau (1762) argues similarly in his Inequality of Man when telling the famous stag-hunt tale.2 However, Kant (1785) is the most famous pedlar of the fallacy. As his categorical imperative puts it: Act only on the maxim that you would at the same time will to be a universal law.

5. Summary This lecture has been an attack on Bayesianism, which I see as a meta-physical doctrine that hinders advances in the foundations of game theory. The lecture began with an appeal to the authority of Savage. It continued with an attempt to explain how it can be shown that certain universes of discourse cannot be completable in the sense required to legitimize a Bayesianismist methodology. It concluded with a brief discussion of some of the implications of looking seriously at the idea that decision-making should be described in terms of algorithms.

We examine an evolutionary model in which the primary source of "noise" that moves the model between equilibria is not random, arbitrarily improbable mutations but mistakes in learning. We find conditions under which the payoff-dominant equilibrium in a 2 x 2 game is selected by the model as well as conditions under which the risk-dominant equilibrium is selected. The relevant risk-dominance considerations, however, arise not in the original game but in a "fitness game" derived from the process by which payoffs in the original game are translated into evolutionary fitnesses. We also find that waiting times until the limiting distribution is reached can be shorter than in a mutation-driven model. To explore the robustness of the results to the specification of the model, we present a number of comparative static results as well as a "two- tiered"evolutionary model in ehich the rules by which agents learn to play the game are themselves subject to evolutionary pressure. Journal of Economic Literature Classification Number C70.

The literature on refinements of Nash equilibirum is now generally acknowledged to have failed in its task of providing a viable equilibrium selection theory for games. Part of the reason for its failure lies in its shaky foundations as a theory of rational behaviour. Backward induction is a particularly doubtful rationality principle. This paper uses the Centipede Game as a setting within which to explain why Aumann's recent attempt to rehabilitate backward induction is unsuccessful.

In this consideration of what constitutes a just society, Sen argues for a comparative perspective that offers grounds for choosing among the alternatives people actually face.

Book description: There has been a great deal of interaction among game theorists, philosophers and logicians in certain foundational problems concerning rationality, the formalization of knowledge and practical reasoning, and models of learning and deliberation. This volume brings together the work of some of the pre-eminent figures in their respective disciplines, all of whom are engaged in research at the forefront of their fields. Together they offer a conspectus of the interaction of game theory, logic and epistemology in the formal models of knowledge, belief, deliberation and learning, and in the relationship between Bayesian decision theory and game theory, as well as between bounded rationality and computational complexity.

Publisher Summary This chapter focuses on the noncooperative models of bargaining. John Nash's (1950) path- breaking paper introduces the bargaining problem, and his pioneering work on noncooperative bargaining theory was taken up again and developed by numerous authors. The target of such a noncooperative theory of bargaining is to find theoretical predictions of what agreement, if any, will be reached by the bargainers, thereby to explain the manner in which the bargaining outcome depends on the parameters of the bargaining problem and to shed light on the meaning of some of the verbal concepts that are used when bargaining is discussed in ordinary language. Three directions in which progress has been particularly fruitful are (1) sequential models have been introduced in studying specific bargaining procedures, (2) refinements of Nash equilibrium have been applied, and (3) bargaining models have been embedded in market situations to provide insights into markets with decentralized trading. In spite of this progress, important challenges are still ahead. The most pressing is that of establishing a properly founded theory of bargaining under incomplete information. A resolution of this difficulty must presumably await a major breakthrough in the general theory of games of incomplete information. From the perspective of economic theory in general, the main challenge remains the modeling of trading institutions (with the nature of money as the most obvious target).

This paper may be read in two different ways. It can be seen as a contribution to the literature on the evolution of bargaining conventions. (See, for example, Young [11].) Those who are interested only in this aspect of the paper will wish to read only Section 2. However, the chief motivation for writing the paper is to round off a philosophical point about the evolution of utilitarianism raised in an earlier paper (Binmore [4]).

This paper argues that the human species has two natural coordination mechanisms: leadership and fairness. A leader who ignores fairness when coordinating the behavior of a large organization risks creating the conditions for the emergence of a destabilizing subgroup that is able to coalesce using fairness as its coordinating device.

In Volume 1 of Game Theory and the Social Contract, Ken Binmore restated the problems of moral and political philosophy in the language of game theory. In Volume 2, Just Playing, he unveils his own controversial theory, which abandons the metaphysics of Immanuel Kant for the naturalistic approach to morality of David Hume. According to this viewpoint, a fairness norm is a convention that evolved to coordinate behavior on an equilibrium of a society's Game of Life. This approach allows Binmore to mount an evolutionary defense of Rawls's original position that escapes the utilitarian conclusions that follow when orthodox reasoning is applied with the traditional assumptions. Using ideas borrowed from the theory of bargaining and repeated games, Binmore is led instead to a form of egalitarianism that vindicates the intuitions that led Rawls to write his Theory of Justice. Written for an interdisciplinary audience, Just Playing offers a panoramic tour through a range of new and disturbing insights that game theory brings to anthropology, biology, economics, philosophy, and psychology. It is essential reading for anyone who thinks it likely that ethics evolved along with the human species.