Extensive-Form Perfect Equilibrium Computation in Two-Player Games

No. 1: Thirty-First AAAI Conference On Artificial Intelligence

Volume

Proceedings of the AAAI Conference on Artificial Intelligence, 31

AAAI Technical Track: Game Theory and Economic Paradigms

We study the problem of computing an Extensive-Form Perfect Equilibrium (EFPE) in 2-player games. This equilibrium concept refines the Nash equilibrium requiring resilience with respect to a specific vanishing perturbation, representing Êmistakes of the players at each decision node. The scientific challenge is intrinsic to the EFPE definition: it requires a perturbation over the agent form, but the agent form is computationally inefficient due to the presence of highly nonlinear constraints. We show that the sequence form can be exploited in a non-trivial way and that, for general-sum games, finding an EFPE is equivalent to solving a suitably perturbed linear complementarity problem. We prove that Lemke's algorithm can be applied, showing that computing an EFPE is PPAD-complete. In the notable case of zero-sum games, the problem is in FP and can be solved by linear programming.ÊOur algorithms also allow one to find a Nash equilibrium when players cannot perfectly control their moves, being subject to a given execution uncertainty, as is the case in most realistic physical settings.

10.1609/aaai.v31i1.10571