Coordination, Timing and Common Knowledge

We sometimes choose to do things only because other people are doing them. David Hume referred to the behavior chosen in such situations as conventions. A leading example of a convention for Hume and philosophers following him was language. Since everyone else uses the word "cat" to refer a cat and the word "dog" to refer to a dog, I also do so, but if everyone was using "cat" to refer to a dog and "dog" to refer to a cat, then I would surely have an incentive to switch to the latter usage. Modern game theory describes such situations as coordination games and the existence of multiple stable conventions as multiple equilibria. Coordination problems are ubiquitous in many important socially contexts. The importance of incentives to coordinate, or strategic complementarities, has been highlighted in recent years by the global …nancial crisis. Lenders from the shadow banking sector had an incentive to lend less if others were lending less (via various economic channels), giving rise to strategic complementarities, or coordination incentives, that exacerbated the market freeze. Holders of European sovereign debt had an incentive to hold less debt if others were holding less, since this would drive up interest rates and thus increase the likelihood of default. The paper was prepared for the June 2103 Ca’Foscari University of Venice International Workshop in Economic Theory on "Where Do We Stand"? I am grateful to Yoram Moses for a conversation where he …rst explained the relation between timing and common knowledge to me, and for comments on this paper. This conversation led me to write a 1995 unpublished paper on "Co-operation and Timing" (Morris (1995)); this paper encompasses and generalizes that working paper.