Solving zero-sum extensive-form games with arbitrary payoff uncertainty models

Abstract: Modeling strategic conflict from a game theoretical perspective involves dealing with epistemic uncertainty. Payoff uncertainty models are typically restricted to simple probability models due to computational restrictions. Recent breakthroughs AI research applied to Poker have resulted in novel approximation approaches such as counterfactual regret minimization, that can successfully deal with large-scale imperfect games. By drawing from these ideas, this work addresses the problem of arbitrary continuous payoff distributions. We propose a method, Harsanyi-Counterfactual Regret Minimization, to solve two-player zero-sum extensive-form games with arbitrary payoff distribution models. Given a game $\Gamma$, using a Harsanyi transformation we generate a new game $\Gamma^#$ to which we later apply Counterfactual Regret Minimization to obtain $\varepsilon$-Nash equilibria. We include numerical experiments showing how the method can be applied to a previously published problem.