Model Checking Strategic Equilibria

Solutions concepts are a fundamental tool for the analysis of game-like systems, and as a consequence, much effort has been devoted to the problem of characterising solution concepts using logic. However, one problem is that, to characterise solution concepts such as Nash equilibrium, it seems necessary to refer to strategies in the object language, which tends to complicate the object language. We propose a logic in which we can formulate important properties of games, (and in particular pure-strategy solution concepts) without recourse to naming strategies in the object language. The idea is that instead of using predicates which state that a particular collection of strategies forms a solution, we define formulae of the logic that are true at a state if and only if this state constitutes a particular equilibrium Outcome. We demonstrate the logic by model checking equilibria of strategic games.