Abstract
Aconvention is a state in which agents coordinate their activity, not as the result of an explicit agreement, but because their expectations are aligned so that each individual believes that all will act so as to achieve coordination for mutual benefit. Since agents are said to follow a convention if they coordinate without explicit agreement, the notion raises fundamental questions: (1) Why do certain conventions remain stable over time?, and (2) How does a convention emerge in the first place? In a pioneering study, Lewis (1969) addresses these questions by applyingnoncooperative game theory. Lewis defines a convention as aNash coordination equilibrium of a noncooperative game that issalient, that is, it is somehow conspicuous to the agents so that all expect one another to conform with the equilibrium. This paper presents a new game theoretic definition of conventions, which formalizes the notion of salience and which also generalizes the class of conventions Lewis discusses in his work. I define a convention as acorrelated equilibrium (Aumann 1974, 1987) satisfying apublic intentions criterion: Every agent wants his intended action to becommon knowledge. I argue that many conventions correspond to correlated equilibria that are not Nash equilibria, and that this is consistent with Lewis' general viewpoint. Finally, I argue that game theoretic characterizations of convention, such as Lewis' and my own, help to explain a convention's stability, but that a fully satisfactory account of the emergence of convention requires a theory of equilibrium selection beyond the scope of Lewis' work.
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References
Aumann, R.: 1974, ‘Subjectivity and Correlation in Randomized Strategies’,Journal of Mathematical Economics 1, 67–96.
Aumann, R.: 1987, ‘Correlated Equilibrium as an Expression of Bayesian Rationality’,Econometrica 55, 1–18.
Bicchieri, C.: 1993,Rationality and Coordination, Cambridge University Press, Cambridge.
Brandenburger, A.: 1992, ‘Knowledge and Equilibrium in Games’,Journal of Economic Perspectives 6, 83–101.
Brandenburger, A. and Dekel, E.: 1987, ‘Rationalizability and Correlated Equilibria’,Econometrica 55, 1391–1402.
Brandenburger, A. and Dekel, E.: 1988, ‘The Role of Common Knowledge Assumptions in Game Theory’, in Frank Hahn (ed.),The Economics of Missing Markets. Information and Games, Clarendon Press, Oxford, pp. 46–61.
Crawford, V. P. and Haller, H.: 1990, ‘Learning to Cooperate: Optimal Play in Repeated Coordination Games’,Econometrica 58, 571–595.
Hume, D.: 1888,A Treatise of Human Nature, edited by L. A. Selby-Bigge, Clarendon Press, Oxford.
Kandori, M., Mailath, G. J. and Rob, R.: 1993, ‘Learning, Mutation, and Long Run Equilibria in Games’,Econometrica 61, 29–56.
Lewis, D.: 1969,Convention: A Philosophical Study, Harvard University Press, Cambridge, Massachusetts.
Luce, R. D and Raiffa, H.: 1957,Games and Decisions: Introduction and Critical Survey, Wiley Publications, New York.
Quine, W. V.: 1936, ‘Truth by Convention’, in O. H. Lee (ed.),Philosophical Essays for A. N. Whitehead, Longmans, New York. Reprinted in Paul Benacerraf and Hilary Putnam (eds.),Philosophy of Mathematics: Selected Readings, 2nd. ed., Cambridge University Press, Cambridge, 1985, pp. 329–354.
Schelling, T.: 1960,The Strategy of Conflict, Harvard University Press, Cambridge, Massachusetts.
Shubik, M.: 1982,Game Theory in the Social Sciences, The MIT Press, Cambridge, Massachusetts.
Skyrms, B.: 1990,The Dynamics of Rational Deliberation, Harvard University Press, Cambridge, Massachusetts.
Skyrms, B.: 1991, ‘Inductive Deliberation, Admissible Acts, and Perfect Equilibrium’, in M. Bacharach and S. Hurley (eds.),Essays in the Foundations of Rational Decision, Blackwell, Oxford, pp. 220–241.
Vanderschraaf, P. and Skyrms, B.: 1993, ‘Deliberational Correlated Equilibria’. Technical Report Series, Report No. MBS 93-07, Irvine Research Unit in Mathematical Behavioral Sciences.
von Neumann, J. and Morgenstern, O.: 1944,Theory of Games and Economic Behavior, Princeton University Press, Princeton.
Young, H. P.: 1993, ‘The Evolution of Conventions’,Econometrica 61, 57–84.
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I thank Cristina Bicchieri, Vince Crawford, Greg Kavka, Brian Skyrms, and an anonymous referee for their many helpful comments on earlier versions of this essay. I would also like to express my gratitude to the U. C. Irvine Focused Research Programs in Public Choice and Scientific Explanation and the Sarah Scaife Foundation for funding the research leading to this essay.
[T]his may properly enough be call'd a convention or agreement betwixt us, tho' without the interposition of a promise; since the actions of each of us have a reference to those of the other, and are perform'd upon the supposition, that something is to be perform'd on the other part. Two men, who pull the oars of a boat, do it by an agreement or convention, tho' they have never given promises to each other.⋯ In like manner are languages gradually establish'd by human conventions without any promise. In like manner do gold and silver become the common measures of exchange, and are esteem'd sufficient payment for what is of a hundred times their value.
David Hume,A Treatise of Human Nature.
Hume (1888, p. 490).
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Vanderschraaf, P. Convention as correlated equilibrium. Erkenntnis 42, 65–87 (1995). https://doi.org/10.1007/BF01666812
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DOI: https://doi.org/10.1007/BF01666812