Knowledge and Convention

This paper investigates the epistemic assumptions that David Lewis makes in his account of social conventions. In particular, I focus on the assumption that the agents have common knowledge of the convention to which they are parties. While evolutionary analyses show that the common knowledge assumption is unnecessary in certain classes of games, Lewis’ original account (and, more recently, Cubitt and Sugden’s reconstruction of it) stresses the importance of including it in the definition of convention. I discuss arguments pro et contra, and conclude that, although the assumption might be relevant to a descriptively adequate account of social convention, it is not required for its rational reconstruction. I then point out that Lewis’ account, properly speaking, is of common reason to believe, rather than of common knowledge, and argue that, in order to formalize aptly the distinction between reason to believe and belief, standard formal epistemic models need to be supplemented with so-called awareness structures. Finally, I stress that the notion of knowledge implicit in Lewis’ text involves interesting elements that cannot be captured in the standard propositional formalizations, but need the full expressive force of quantified epistemic logic. 1 Lewis on convention Perhaps the most important insight in Lewis’ account of convention is the idea that games of coordination lie at the core of the notion of convention. In coordination games players’ interests (roughly) coincide while in zerosum games the interest of the players are always opposed Thus, coordination problems (non-trivial, in that they possess more than one strict Nash equilibrium) underlie every convention, since a convention is one particular recurrent equilibrium of such games. 1 The distinction was pointed out a few years before Convention by Thomas Schelling, cf. [Sch60], p. 84: “If the zero-sum game is the limiting case of pure conflict, what is the other extreme? It must be the “pure collaboration” game in which players win or lose together, having identical preferences regarding the outcome.”