Knowledge was traditionally held to be justiﬁed true belief. This paper examines the implications of maintaining this view if justication is interpreted algorithmically. It is argued that if we move suﬃciently far from the small worlds to which Bayesian decision theory properly applies, we can steer between the rock of fallibilism and the whirlpool of skepticism only by explicitly building into our framing of the underlying decision problem the possibility that its attempt to describe the world is inadequate.
Do conventions need to be common knowledge? David Lewis builds this requirement into his deﬁnition of a convention. This paper explores the extent to which his approach ﬁnds support in the game theory literature. The knowledge formalism developed by Robert Aumann and others militates against Lewis’s approach, because it demonstrates that it is almost impossible for something to become common knowledge in a large society. On the other hand, Ariel Rubinstein’s Email Game suggests that coordinated action is equally hard for (...) rational players. But an unnecessary simplifying assumption in the Email Game turns out to be doing all the work, and the paper concludes that common knowledge is better excluded from a deﬁnition of the conventions that we use to regulate our daily lives. (shrink)
This commentary on the paper “Economic Man” in Cross-Cultural Perspective  is ﬁercely critical, but the criticism is not directed at the anthropological ﬁeld work reported in the paper, which seems to me entirely admirable. The criticism is directed at the editorial rhetoric that accompanies the scientiﬁc reports of the experiments carried out in the ﬁfteen small-scale societies studied. The rhetoric is markedly more subdued than in the book Foundations of Human Sociality  from which the current paper is extracted. (...) (See Samuelson  for a review.) However, the claim remains that “economic man” is an experimental failure, and that we must seek an alternative paradigm. This paper argues that the editors’ enthusiasm for this perennially popular claim has led them into two mistakes. Philosophers call the ﬁrst mistake the ignoratio elenchi—the refuting of propositions that your opponent does not maintain. In particular, it is not axiomatic in orthodox economic theory that human beings are selﬁsh. Even if such a proposition were axiomatic, the backward induction principle the authors use when analyzing the Ultimatum Game would not follow. The second mistake is that of neglecting to report data that does not support their claims about “economic man”. In particular, although it is not axiomatic in mainstream economics that human beings maximize their own income, there is a huge experimental literature whose results are consistent with the hypothesis that most people behave in this way after gaining suﬃcient experience of most tasks they are set in the laboratory. As a result of these mistakes, the editors contrive to treat conclusions of their study that are broadly supportive of the game-theoretic approach to social norms as though they were inconsistent with the principles on which game theory is based. (shrink)
’Tis vain to talk of adding quantities which after the addition will continue to be as distinct as they were before; one man’s happiness will never be another man’s happiness: a gain to one man is no gain to another: you might as well pretend to add 20 apples to 20 pears.
This paper argues that we need to look beyond Bayesian decision theory for an answer to the general problem of making rational decisions under uncertainty. The view that Bayesian decision theory is only genuinely valid in a small world was asserted very ﬁrmly by Leonard Savage  when laying down the principles of the theory in his path-breaking Foundations of Statistics. He makes the distinction between small and large worlds in a folksy way by quoting the proverbs ”Look before you (...) leap” and ”Cross that bridge when you come to it”. You are in a small world if it is feasible always to look before you leap. You are in a large world if there are some bridges that you cannot cross before you come to them. As Savage comments, when proverbs conﬂict, it is proverbially true that there is some truth in both—that they apply in diﬀerent contexts. He then argues that some decision situations are best modeled in terms of a small world, but others are not. He explicitly rejects the idea that all worlds can be treated as small as both ”ridiculous” and ”preposterous”. The ﬁrst half of his book is then devoted to a very successful development of the set of ideas now known as Bayesian decision theory for use in small worlds. The second half of the book is an attempt to develop a quite diﬀerent set of ideas for use in large worlds, but this part of the book is usually said to be a failure by those who are aware of its existence.2 Frank Knight  draws a similar distinction between making decision under risk or uncertainty.3 The pioneering work of Gilboa and Schmeidler  on making.. (shrink)
My answer to the question why? is relatively uncontroversial among anthropologists. Sharing food makes good evolutionary sense, because animals who share food thereby insure themselves against hunger. It is for this reason that sharing food is thought to be so common in the natural world. The vampire bat is a particularly exotic example of a food-sharing species. The bats roost in caves in large numbers during the day. At night, they forage for prey, from whom they suck blood if they (...) can, but they aren’t always successful. If they fail to obtain blood for several successive nights, they die. The evolutionary pressure to share blood is therefore strong. The biologist Wilkinson  reports that a hungry bat begs for blood from a roostmate, who will sometimes respond by regurgitating some of the blood it is carrying in its own stomach. This isn’t too surprising when the roostmates are related, but the bats also share blood with roostmates who aren’t relatives. The behaviour is nevertheless evolutionarily stable, because the sharing is done on a reciprocal basis, which means that a bat is much more likely to help out a roostmate that has helped it out in the past. Bats that refuse to help out their fellows therefore risk not being helped out themselves in the future. Vampire bats have their own way of sharing, and we have ours. We call our way of sharing “fairness”. If the accidents of our evolutionary history had led to our sharing in some other way, it would not occur to us to attribute some special role to our current fairness norms. Whatever alternative norms we then.. (shrink)
The coverage is based on a research paper Insidious Discrimination? Disentangling the Beauty Premium on a Game Show which examined the strategic behaviour of participants on a Dutch TV game show Shafted.
This paper oﬀers an experimental test of a version of Rubinstein’s bargaining model in which the players’ discount factors are unequal. We ﬁnd that learning, rationality, and fairness are all signiﬁcant in determining the outcome. In particular, we ﬁnd that a model of myopic optimization over time predicts the sign of deviations in the opening proposal from the ﬁnal undiscounted agreement in the previous period rather well. To explain the amplitude of the deviations, we then successfully ﬁt a perturbed version (...) of the model of myopic adjustment to the data that allows for a bias toward refusing inequitable oﬀers. (shrink)
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 Schmidt1 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? (shrink)
This short paper begins with a summary of the views of a sympathetic game theorist on the current state of play in what is still called the New Institutional Economics. It continues with a much abbreviated summary of my own attempts to treat justice as a kind of institution in the hope that this will serve as a case study in how game theory can serve as a useful intellectual framework for the study of human institutions.
When judging what is fair, how do we decide how much weight to assign to the conflicting interests of different classes of people? This subject has received some attention in a utilitarian context, but has been largely neglected in the case of egalitarian societies of the kind studied by John Rawls. My Game Theory and the Social Contract considers the problem for a toy society with only two citizens. This paper examines the theoretical difficulties in extending the discussion to societies (...) with more than two citizens. (shrink)
This article is my latest attempt to come up with a minimal version of my evolutionary theory of fairness (Binmore [11, 10, 8, 9]). The naturalism that I espouse is currently unpopular, but Figure 1 shows that the scientific tradition in moral philosophy nevertheless has a long and distinguished history. John Mackie  has been its most eloquent spokesman in modern times. His demolition of the claims made for a priori reasoning in moral philosophy seem unanswerable to me. In (...) Mackie’s view, human morality is an artefact of our evolutionary history. To study it, he tells us to look at the anthropological facts presented in such pioneering studies as Westermarck’s  Origin and Development of the Moral Ideas. And for a framework within which to make sense of such anthropological data, he directs our attention to Von Neumann’s theory of games. (shrink)
Do conventions need to be common knowledge in order to work? David Lewis builds this requirement into his definition of a convention. This paper explores the extent to which his approach finds support in the game theory literature. The knowledge formalism developed by Robert Aumann and others militates against Lewis’s approach, because it shows that it is almost impossible for something to become common knowledge in a large society. On the other hand, Ariel Rubinstein’s Email Game suggests that coordinated action (...) is no less hard for rational players without a common knowledge requirement. But an unnecessary simplifying assumption in the Email Game turns out to be doing all the work, and the current paper concludes that common knowledge is better excluded from a definition of the conventions that we use to regulate our daily lives. (shrink)
Experimental results on the Ellsberg paradox typically reveal behavior that is commonly interpreted as ambiguity aversion. The experiments reported in the current paper find the objective probabilities for drawing a red ball that make subjects indifferent between various risky and uncertain Ellsberg bets. They allow us to examine the predictive power of alternative principles of choice under uncertainty, including the objective maximin and Hurwicz criteria, the sure-thing principle, and the principle of insufficient reason. Contrary to our expectations, the principle of (...) insufficient reason performed substantially better than rival theories in our experiment, with ambiguity aversion appearing only as a secondary phenomenon. (shrink)
Robert Aumann argues that common knowledge of rationality implies backward induction in finite games of perfect information. I have argued that it does not. A literature now exists in which various formal arguments are offered in support of both positions. This paper argues that Aumann's claim can be justified if knowledge is suitably reinterpreted.
Some behavioral economists argue that the honoring of social norms can be adequately modeled as the optimization of social utility functions in which the welfare of others appears as an explicit argument. This paper suggests that the large experimental claims made for social utility functions are premature at best, and that social norms are better studied as equilibrium selection devices that evolved for use in games that are seldom studied in economics laboratories.
Games are everywhere: Drivers manoeuvring in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. A firm negotiating next year's wage is playing a bargaining game. The opposing candidates in an election are playing a political game. The supermarket's price for corn flakes is decided by playing an economic game. -/- Game theory is about how to play such games in a rational way. Even when the players have not thought everything out (...) in advance, game theory often works for the same reason that mindless animals sometimes end up behaving very cleverly: evolutionary forces eliminate irrational play because it is unfit. -/- Game theory has seen spectacular successes in evolutionary biology and economics, and is beginning to revolutionize other disciplines from psychology to political science. This Very Short Introduction introduces the fascinating world of game theory, showing how it can be understood without mathematical equations, and revealing that everything from how to play poker optimally to the sex ratio among bees can be understood by anyone willing to think seriously about the problem. (shrink)
Can people be relied upon to be nice to each other? Thomas Hobbes famously did not think so, but his view that rational cooperation does not require that people be nice has never been popular. The debate has continued to simmer since Joseph Butler took up the Hobbist gauntlet in 1725. This article defends the modern version of Hobbism derived largely from game theory against a new school of Butlerians who call themselves behavioral economists. It is agreed that the experimental (...) evidence supports the claim that most people will often make small sacrifices on behalf of others and that a few will sometimes make big sacrifices, but that the larger claims made by contemporary Butlerians lack genuine support. Key Words: natural justice fairness social norms game theory behavioral economics. (shrink)
A persistent argument against the transitivity assumption of rational choice theory postulates a repeatable action that generates a significant benefit at the expense of a negligible cost. No matter how many times the action has been taken, it therefore seems reasonable for a decision-maker to take the action one more time. However, matters are so fixed that the costs of taking the action some large number of times outweigh the benefits. In taking the action some large number of times on (...) the grounds that the benefits outweigh the costs every time, the decision-maker therefore reveals intransitive preferences, since once she has taken it this large number of times, she would prefer to return to the situation in which she had never taken the action at all. We defend transitivity against two versions of this argument: one in which it is assumed that taking the action one more time never has any perceptible cost, and one in which it is assumed that the cost of taking the action, though (sometimes) perceptible, is so small as to be outweighed at every step by the significant benefit. We argue that the description of the choice situation in the first version involves a contradiction. We also argue that the reasoning used in the second version is a form of similarity-based decision-making. We argue that when the consequences of using similarity-based decision-making are brought to light, rational decision-makers revise their preferences. We also discuss one method that might be used in performing this revision. (shrink)
The target article by Henrich et al. describes some economic experiments carried out in fifteen small-scale societies. The results are broadly supportive of an approach to understanding social norms that is commonplace among game theorists. It is therefore perverse that the rhetorical part of the paper should be devoted largely to claiming that “economic man” is an experimental failure that needs to be replaced by an alternative paradigm. This brief commentary contests the paper's caricature of economic theory, and offers a (...) small sample of the enormous volume of experimental data that would need to be overturned before “economic man” could be junked. (shrink)
This article is extracted from a forthcoming book, Natural Justice. It is a nontechnical introduction to the part of game theory immediately relevant to social contract theory. The latter part of the article reviews how concepts such as trust, responsibility, and authority can be seen as emergent phenomena in models that take formal account only of equilibria in indefinitely repeated games. Key Words: game theory equilibrium evolutionary stability reciprocity folk theorem trust altruism responsibility (...) authority. (shrink)