Semi-stationary Equilibrium Strategies in Non-cooperative N-person Semi-Markov Games
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For a limiting ratio average (undiscounted) non-cooperative N-person semi-Markov game with finite state and action spaces, we prove that the solutions in the game where all players are restricted to semi-stationary strategies (that depend only on the initial state and the current state) are solutions for the unrestricted game. Furthermore, we consider zero-sum two-person semi-Markov games with action independent transitions (where the transition probabilities are independent of the actions of the players in each state) and prove the existence of an optimal semi-stationary strategy for each player. An example is provided to show that the semi-stationary optimal strategies cannot be strengthened further for such class of games.
KeywordsSemi-Markov games Limiting ratio average payoff Nash equilibrium Action independent transitions Optimal semi-stationary strategies
Mathemetics Subject Classification (2000)Primary: 91A15 Secondary: 60G99
The authors wish to thank the unknown referees who have patiently gone through this paper and whose suggestions have improved its presentation and readability considerably.
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