Knowledge, Equilibrium and Convention

Abstract

There are two general classes of social conventions: conventions of coordination, and conventions of partial conflict. In coordination problems, the interests of the agents coincide, while in partial conflict problems, some agents stand to gain only if other agents unilaterally make certain sacrifices. Lewis' (1969) pathbreaking analysis of convention in terms of game theory focuses on coordination problems, and cannot accommodate partial conflict problems. In this paper, I propose a new game-theoretic definition of convention which generalizes previous game-theoretic definitions (Lewis 1969, Vanderschraaf 1995), and which can be used to characterize norms of justice in partial conflict situations. I argue that the key structural property necessary for a social arrangement to be a convention is that it be conditionally self-enforcing, in the sense that: (i) each agent has a decisive reason to follow her end of the arrangement given that she expects all to do likewise, (ii) given a different set of expectations, some agents would have had a decisive reason to deviate, and (iii) these facts are common knowledge. This leads to a definition of convention as a strict correlated equilibrium (Aumann 1974) together with appropriate common knowledge conditions. Examples are given in which it is shown how this more general account of convention can be used to analyze norms of justice as well as coordination problems.

It is only a general sense of common interest; which sense all the members of the society express to one another, and which induces them to regulate their conduct by certain rules. I observe, that it will be for my interest to leave another in the possession of his goods, provided he will act in the same manner with regard to me. He is sensible of a like interest in the regulation of his conduct. When this common sense of interest is mutually express'd, and is known to both, it produces a suitable resolution and behavior. And this may properly be call'd a convention or agreement betwixt us,...

David Hume, A Treatise of Human Nature

And so it goes — we're here because we're here because we're here because we're here. Once the process gets started, we have a metastable self-perpetuating system of preferences, expectations, and actions capable of persisting indefinitely. As long as uniform conformity is a coordination equilibrium, so that each wants to conform conditionally upon coordination by the others, conforming action produces expectation of conforming action and expectation of conforming action produces conforming action.

This is the phenomenon I call convention.