Verifying Equilibria in Games of Complete and Perfect Information Represented by Presburger Formulas

Given a description of a game and a strategy profile, we are interested in the problem of deciding if the strategy profile is an equilibrium of the game. In the present paper we restrict our attention to games of complete but imperfect information. The game is represented by a sequence of Presburger formulas and the equilibrium property is checked by computing conservative approximate least fixpoints using abstract interpretation. This work has applications in open multi-agent systems, where agents will need to be able to verify that a recommended strategy profile is an equilibrium of a game.