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Rationality and Coordination.

Brian Skyrms Department of Philosophy, University of California, Irvine

This is an important book on the interface between philosophy, game theory, and economics. The idea that rational choice may illuminate the theory of the social contract is as old as Hobbes; the criticism that rational choice is not the whole story is as old as Hume. After von Neumann and Morgenstern [1947] made great advances in the theory of interacting rational choices, it was not long before John Rawls [1957] applied their ideas to a theory of justice. Bicchieri's book stands in this tradition. Recent advances in decision theory and game theory are brought to bear on problems of coordination, convention, and the social contract. But Bicchieri is sceptical of highly idealized assumptions about knowledge, common knowledge, and rationality. She prefers to work with models of bounded rationality, and to supplement bounded rationality with dynamics of learning, belief revision, and cultural evolution. From Bicchieri's point of view, philosophy has something to offer game theory and economics as well as something to learn from them.

The first chapter deals with rational choice. In what sense can the hypothesis that individuals make rational choices explain macrophenomena in economics, sociology, and political science. Bicchieri focuses on rational belief formation and distinguishes between various grades of rational belief, from consistency to a well-calibrated state in which subjective probabilities coincide with objective chances. The 'rational expectations hypothesis' is taken to be that agents will get themselves to the latter strongly rational state. The hypothesis is criticized in that it depends on assumptions of a stationary environment and a highly efficacious adaptive process to deliver the goods.

The second chapter questions the adequacy of rationality as a foundation for the Nash equilibrium concept of game theory. She points out that Bayesian rationality - that is, maximizing expected payoff according to one's beliefs - and even common knowledge of Bayesian rationality among the players, are too weak to assure a Nash equilibrium. The relevant game theoretic notions of dominance and rationalizability are introduced. Bicchieri concludes that a bridge between individual rationality and Nash equilibrium requires that traditional game theory be supplemented by a theory of the dynamics of belief.

The examples of Chapter 2 were all in the normal form. Chapter 3 raises the same question in the context of extensive form games. The logic of backward and forward induction and the concepts of perfect and sequential equilibrium are examined. The significance of beliefs off the equilibrium path is discussed, and ideas of Levi [1977] and Gardenfors [1984] regarding belief revision are brought to bear on this issue. However, requiring common knowledge of a particular method of belief revision, on top of common knowledge of Bayesian rationality and the structure of the game, is seen as imposing unreasonable demands on the players.

Chapter 4 argues that such all-encompassing common knowledge assumptions are not required for solutions of finite extensive form games, and that, for some simple extensive form games of interest, just a few knowledge levels will do. Bicchieri also argues that if one does make very strong common knowledge assumptions, then it is surprisingly easy to slip in enough assumptions to generate inconsistency.

Chapter 5 shifts focus to situations in which rational individuals have only limited knowledge of their mutual rationality and perhaps also of the structure of the game. In this kind of situation many more outcomes of play are possible. In particular, various types of behaviour which have been loosely been described as 'irrational' are seen to be quite compatible with this setup. The iterated Prisoner's Dilemma and the Chain Store paradox figure as examples and the work of Kreps, Wilson, Milgrom, and Roberts is discussed (Kreps, D., Milgrom, P., Roberts, J. and Wilson, R. [1982]; Kreps, D. and Wilson, R. [1982]; Kreps, D. and Wilson, R. [1982]; Milgrom, P. and Roberts, J. [1982]).

The final chapter gives an account of how social norms can be established in small groups by the dynamics of learning, and then how they can spread throughout a large population by a process of cultural evolution. In particular, it is shown how for players in a finitely repeated Prisoner's Dilemma, who are limited to the simple 'Markov habits' that I discuss elsewhere Skyrms [1990], norms of cooperation can arise and spread.

This book is well informed and well written. Bicchieri is familiar with contemporary work in economics and game theory. The book, however, is written in a way that does not presuppose any background in these areas. I am in general agreement with Bicchieri's criticisms of traditional game theory, and I believe that the themes of bounded rationality, learning dynamics, and cultural evolution should and will play an increasingly important role in game theory and its applications in philosophy, political theory and economics. This is a book which deserves to be widely read and discussed.

References

Gardenfors [1984]: 'Epistemic Importance and Minimal Changes in Belief', Australasian Journal of Philosophy, 62, pp. 136-57.

John Rawls [1957]: 'Justice as Fairness', Journal of Philosophy, 54, pp. 653-62.

Kreps, D., Milgrom, P., Roberts, J. and Wilson, R. [1982]: 'Rational Cooperation in Finitely Repeated Prisoner's Dilemma' Journal of Economic Theory, 27, pp. 245-52.

Kreps, D. and Wilson, R. [1982]: 'Sequential Equilibria', Econometrica, 50, pp. 863-94.

Kreps, D. and Wilson, R. [1982]: 'Reputation and Incomplete Information', Journal of Economic Theory, 27, pp. 253-79.

Levi [1977]: 'Subjunctives, Dispositions and Chances', Synthese, 34, pp. 423-55.

Milgrom, P. and Roberts, J. [1982]: 'Predation, Reputation, and Entry Deterrence, Journal of Economic Theory, 27, pp. 280-312.

Morgenstern [1947]: Theory of Games and Economic Behaviour, Princeton: Princeton University Press.

Skyrms [1990]: The Dynamics of Rational Deliberation, Cambridge, MA, Harvard University Press.
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Author:Skyrms, Brian
Publication:The British Journal for the Philosophy of Science
Article Type:Book Review
Date:Dec 1, 1996
Words:938
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