Stochastic Games with Average Cost Constraints
The paper introduces the model of undiscounted stochastic games augmented by side constraints on the levels of a player’s average costs. Several variants of this problem are suggested, and the special case of zero-sum games with constraints on one side is analyzed; under certain recurrence conditions, existence of the value and (non-stationary) optimal strategies are established.
KeywordsNash Equilibrium Average Cost Stationary Strategy Reward Function Stochastic Game
Unable to display preview. Download preview PDF.
- E. Altman and A. Shwartz, “Markov decision problems and state-action frequencies,” SIAM J. Control and Optimization 29 No. 4, July 1991.Google Scholar
- V. S. Borkar, “Controlled Markov chains with constraints,” Proceedings of the Workshop on Recent Advances in Modeling and Control of Stochastic Systems, Bangalore, Jan. 1991.Google Scholar
- D.-J. Ma, A. M. Makowski and A. Shwartz, “Estimation and optimal control for constrained Markov chains,” Proc. 25th IEEE Conf. on Decision and Control, pp. 994–999, 1986.Google Scholar
- N. Shimkin and A. Shwartz, “Guaranteed performance regions in Markovian systems with competing decision makers ,” to appear in IEEE Trans. Automat Contr., Feb. 1993.Google Scholar
- M. A. Stern, On Stochastic Games with Limiting Average Pay-Off. Ph.D. dissertation, University of Illinois, Circle Campus, Chicago, 1975.Google Scholar