Convention as correlated equilibrium

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.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).