Mathematical Sciences: Algorithms and Existence Theorems for Cooperative and Stochastic Games

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This project will study a diverse set of questions in games theory: a) Do Nash equilibria exist for single controller and switching controller games in arbitrary state spaces? b) Do ARAT games and switching control games admit stationary Nash equilibrium for undiscounted games? c) Characterize multi-choice nucleolus by suitably defining Sobolev's reduced subgames; d) Find an efficient algorithm to solve for the nucleolus of flow games, linearly constrained games, and homogeneous games. %%% Methods, techniques and ideas of games theory have applications to economics, operations research, queuing theory, and control theory.