On stationary equilibria of a single-controller stochastic game |
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Authors: | Jerzy A Filar |
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Institution: | (1) Department of Mathematical Sciences, The Johns Hopkins University, 21218 Baltimore, MD, USA |
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Abstract: | We consider a two-person, general-sum, rational-data, undiscounted stochastic game in which one player (player II) controls
the transition probabilities. We show that the set of stationary equilibrium points is the union of a finite number of sets
such that, every element of each of these sets can be constructed from a finite number of extreme equilibrium strategies for
player I and from a finite number of pseudo-extreme equilibrium strategies for player II. These extreme and pseudo-extreme
strategies can themselves be constructed by finite (but inefficient) algorithms. Analogous results can also be established
in the more straightforward case of discounted single-controller games. |
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Keywords: | Stochastic Games Orderfield Property Average Rewards Discounted Rewards Extreme Equilibrium Strategies Finite Algorithms Superharmonic Vector |
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