Mathematical Programming Formulations to Compute Steady States in Two-Player Extensive-Form Games

The most common solution concept for a strategic interaction situation is the Nash equilibrium, in which no agent can do better by deviating unilaterally. However, the Nash equilibrium underlays on the assumption of common information that is hardly verified in many practical situations. When information is not common, rational agents are assumed to learn from their observations to derive beliefs over their opponents' play and payoffs. In these situations, there are steady states composed of beliefs and strategies in which the strategies do not constitute a Nash equilibrium. These stable states are called in the game theory literature self-confirming equilibria. They are such that every agent plays the best response to her beliefs and these are correct on the equilibrium path, while off the equilibrium path they may be incorrect. We present some mathematical programming formulations for computing self-confirming equilibria and its refinements in two-player extensive-form games and we study their properties.