Awareness Equilibrium

We provide a model of awareness in normal-form games with incomplete information. Players and actions are common knowledge but types and probability distribution over these are not. Each player is aware of a subset of types and a joint distribution over these, and holds conjectures about other players’ awareness and conjectures. In an awareness equilibrium, strategies are best replies, and the ensuing outcome is consistent with players’ conjectures. We compare awareness equilibrium outcomes to the outcomes of Bayesian equilibrium with a common prior. In a wide class of well-studied environments (e.g., auctions), the outcomes are the same under both scenarios. In our last example we construct a game where an awareness equilibrium outcome cannot be justified in a Bayesian equilibrium under any prior. JEL: C72, D82, D83 ∗[email protected]; [email protected]. The previous version, August 2006, circulated under the title Awareness as an Equilibrium Notion: Normal-Form Games. A conversation with Leeat Yariv helped us to get started on this project. We are most grateful to Bill Zame for his helpful comments, and we also wish to thank to Ken Binmore, Colin Camerer, Yossi Feinberg, Matt Jackson, George Mailath, Andrea Mattozzi, Debrah Meloso, Motty Perry, and the seminar participants at Essex and Yale.