Determining the Optimal Strategies for Antagonistic Positional Games in Markov Decision Processes
A class of stochastic antagonistic positional games for Markov decision processes with average and expected total discounted costs’ optimization criteria are formulated and studied. Saddle point conditions in the considered class of games that extend saddle point conditions for deterministic parity games are derived. Furthermore, algorithms for determining the optimal stationary strategies of the players are proposed and grounded.
KeywordsNash Equilibrium Payoff Function Markov Decision Process Stationary Strategy Markov Decision Problem
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