Mathematical Sciences: Algorithms and Existence Theorems forStochastic Games in Finite and Arbitrary State Spaces

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This project concerns research in the area of stochastic games, dealing with both zero-sum and non-zero-sum games in finite and arbitrary state spaces. THe value and Nash equilibria in both discounted and undiscounted payoffs are considered. The following are the main problems of this project. 1. Find an efficient algorithm to solve undiscounted switching control stochastic games for value and optimal stationary strategies. 2. Find an efficient algorithm to solve for Nash equilibria when the stochastic game is non-zero-sum and one player controls the law of motion. 3. Find an efficient algorithm to solve for pure optima; stationary strategies in games with perfect information or in games with additive reward and additive transitions. 4. Are there optimal stationary strategies for zero-sum stochastic games with additive transitions? 5. Do switching control non- zero-sum games admit stationary Nash equilibria? 6. Do they possess order field property? Do discounted stochastic games in arbitrary state space and compact action spaces possess Nash equilibria in stationary strategies when they belong to the special structured class such as ARAT, one player control or switching control 8. Do undiscounted zero-sum games of the above structured type possess value in stationary strategies when the state space is arbitrary?