Quadratic programming and the single-controller stochastic game

Abstract

In this paper we show that an optimal solution to an appropriately constructed quadratic program provides a stationary Nash equilibrium point of a two-person, general-sum, single-controller stochastic game. Stochastic games with both the limiting average and the discounted payoff criteria are considered. For the latter, the converse statement also holds; that is, every stationary equilibrium point provides an optimal solution to the quadratic program. The above results include as special cases the known quadratic/linear programming formulations of bimatrix games, matrix games, Markovian decision processes, and single-controller zero-sum stochastic games.