Verifiable Equilibria in Boolean Games

This work is motivated by the following concern. Suppose we have a game exhibiting multiple Nash equilibria, with little to distinguish them except that one of them can be verified while the others cannot. That is, one of these equilibria carries sufficient information that, if this is the outcome, then the players can tell that an equilibrium has been played. This provides an argument for this equilibrium being played, instead of the alternatives. Verifiability can thus serve to make an equilibrium a focal point in the game. We formalise and investigate this concept using a model of Boolean games with incomplete information. We define and investigate three increasingly strong types of verifiable equilibria, characterise the complexity of checking these, and show how checking their existence can be captured in a variant of modal epistemic logic.