Abstract:

In many settings, agents can communicate---either directly or through intermediaries---before they engage in strategic interactions. We explore when such communication can be beneficial in general strategic contexts. This question reduces, for any non-degenerate objective, to determining when Nash equilibria are extreme points within the set of correlated equilibria. Our results demonstrate that any sufficiently random mixed Nash equilibrium, involving at least three players randomizing, can always be improved by either correlating agents' actions or switching to a less random equilibrium, regardless of the underlying objective. As a result, symmetric equilibria in a variety of symmetric environments---such as auctions, voting, and matching---are inherently suboptimal, no matter the goal.