Knowledge and Equilibrium

The basic model we consider works as follows. There are a set of states Ω, one of which is true. For each state ω ∈ Ω, and a given agent, there is a set of states h(ω) that the agent considers possible when the actual state is ω. Finally, we will say that an agent knows E if E obtains at all the states that the agent believes are possible. These basic definitions will provide a language for talking about reasoning and the implications of reasoning.