Stationary, completely mixed and symmetric optimal and equilibrium strategies in stochastic games
Autor: | Nagarajan Krishnamurthy, Sujatha Babu, T. Parthasarathy |
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Rok vydání: | 2016 |
Předmět: |
Statistics and Probability
Computer Science::Computer Science and Game Theory Economics and Econometrics Continuous-time stochastic process Mathematical optimization 021103 operations research Sequential game 010102 general mathematics Symmetric game Stochastic game ComputingMilieux_PERSONALCOMPUTING 0211 other engineering and technologies Symmetric equilibrium TheoryofComputation_GENERAL 02 engineering and technology 01 natural sciences Mathematics (miscellaneous) Strategy Transpose Repeated game 0101 mathematics Statistics Probability and Uncertainty Social Sciences (miscellaneous) Mathematics |
Zdroj: | International Journal of Game Theory. 46:761-782 |
ISSN: | 1432-1270 0020-7276 |
Popis: | In this paper, we address various types of two-person stochastic games—both zero-sum and nonzero-sum, discounted and undiscounted. In particular, we address different aspects of stochastic games, namely: (1) When is a two-person stochastic game completely mixed? (2) Can we identify classes of undiscounted zero-sum stochastic games that have stationary optimal strategies? (3) When does a two-person stochastic game possess symmetric optimal/equilibrium strategies? Firstly, we provide some necessary and some sufficient conditions under which certain classes of discounted and undiscounted stochastic games are completely mixed. In particular, we show that, if a discounted zero-sum switching control stochastic game with symmetric payoff matrices has a completely mixed stationary optimal strategy, then the stochastic game is completely mixed if and only if the matrix games restricted to states are all completely mixed. Secondly, we identify certain classes of undiscounted zero-sum stochastic games that have stationary optima under specific conditions for individual payoff matrices and transition probabilities. Thirdly, we provide sufficient conditions for discounted as well as certain classes of undiscounted stochastic games to have symmetric optimal/equilibrium strategies—namely, transitions are symmetric and the payoff matrices of one player are the transpose of those of the other. We also provide a sufficient condition for the stochastic game to have a symmetric pure strategy equilibrium. We also provide examples to show the sharpness of our results. |
Databáze: | OpenAIRE |
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