Finding Equilibrium in Multi-Agent Games with Payoff Uncertainty

We study the problem of finding equilibrium strategies in multi-agent games with incomplete payoff information, where the payoff matrices are only known to the players up to some bounded uncertainty sets. In such games, an ex-post equilibrium characterizes equilibrium strategies that are robust to the payoff uncertainty. When the game is one-shot, we show that in zero-sum polymatrix games, an ex-post equilibrium can be computed efficiently using linear programming. We further extend the notion of ex-post equilibrium to stochastic games, where the game is played repeatedly in a sequence of stages and the transition dynamics are governed by an Markov decision process (MDP). We provide sufficient condition for the existence of an ex-post Markov perfect equilibrium (MPE). We show that under bounded payoff uncertainty, the value of any two-player zero-sum stochastic game can be computed up to a tight value interval using dynamic programming.