Nonlinear programming and stationary equilibria in stochastic games (Q1176577)

A stochastic game is a dynamic programming situation (with infinite horizon) in which more than one decision maker influences the path the system follows, each decision maker (= player) receiving his own immediate reward. In this paper three nonlinear programming problems are given which solve the following problems. A solution of the first NLP gives an equilibrium strategy for \(\beta\)-discounted \(n\)-person stochastic games. The solvability of the second NLP is equivalent with the existence of stationary equilibrium strategies for \(n\)-person limiting average stochastic games. Finally, the authors give an NLP for finding \(\varepsilon\)-optimal strategies for 2-person zero-sum stochastic games under the limiting average payoff criterium. The authors do not discuss the question how the rather complicated NLP's can be solved.