Approximations in dynamic zero-sum games

The authors develop a unifying approach for approximating a ‘limit’ zero-sum game by a sequence of approximating games. They discuss both the convergence of the values and the convergence of optimal (or ‘almost’ optimal) strategies. Moreover, based on optimal policies for the limit game, the authors construct policies which are almost optimal for the approximating games. They then apply the general framework to state approximations of stochastic games, to convergence of finite horizon problems to infinite horizon problems, and to convergence in the discount factor and in the immediate reward.