Abstract
This paper treats of nonzero-sum discounted stochastic games with general state space where the players are allowed to use correlated strategies. The concept of correlated weak equilibrium of Moulin and Vial (being an extension of the Nash equilibrium point) is adopted to such games. An existence theorem is proved for a class of discounted stochastic games with a Borel state space where stationary Nash equilibria are not known to exist.
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This paper was presented at the International Workshop on Stochastic Games organized by Prof. T. E. S. Raghavan at the University of Illinois at Chicago in June 26-28, 1987.
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References
Aumann, R. J. (1974). Subjectivity and Correlation in Randomized Strategies, J. Math. Economics 1, 67–96.
Balder, E. J. (1988). Generalized Equilibrium Results for Games with Incomplete Information, Math. Oper. Res. 13, 265–276.
Bertsekas, D. P. and S. E. Shreve (1978). Stochastic Optimal Control: The Discrete Time Case, Academic Press, New York.
Blackwell, D. (1965). Discounted Dynamic Programming, Ann. Math. Statist. 36, 226–235.
Dunford, N. and J. T. Schwartz (1958). Linear Operators, Vol. I, Interscience Publishers, New York.
Himmelberg, C. J., T. Parthasarathy, T. E. S. Raghavan and F. S. Van Vleck (1976). Existence of p-Equilibrium and Optimal Stationary Strategies in Stochastic Games, Proc. Amer. Math. Soc. 60, 245–251.
Ionescu-Tulcea, A. and C. (1969). Topics in the Theory of Lifting, Springer-Verlag, Berlin.
Moulin, H. (1981). Theorie des Jeux pour L’Économie et la Politique, Hermann, Paris.
Moulin, H. and J. P. Vial (1978). Strategically Zero-Sum Games: the Class of Games whose Completely Mixed Equilibria Cannot Be Improved upon, Internat. J. Game Theory 7, 201–221.
Nowak, A. S. (1985). Existence of Equilibrium Stationary Strategies in Discounted Noncooperative Stochastic Games with Uncountable State Space, J. Optim. Theory Appl. 45, 591–602.
Nowak, A. S. (1987). Nonrandomized Strategy Equilibria in Noncooperative Stochastic Games with Additive Transition and Reward Structure, J. Optim. Theory Appl. 52, 429–441.
Parthasarathy, T. (1982). Existence of Equilibrium Stationary Strategies in Discounted Stochastic Games, Sankhya: The Indian J. Statist. Ser. A 44, 114–127.
Parthasarathy, T. and S. Sinha (1987). Equilibrium Strategies in Nonzero-Sum Discounted Stochastic Games with Uncountable State Space and State Independent Transitions, Preprint, Indian Statistical Institute, New Delhi.
Rieder, U.(1979). Equilibrium Plans for Nonzero-Sum Markov Games, in: Game Theory and Related Topics, Edited by O. Moeschlin and D Pallaschke, North-Holland, Amsterdam.
Shapley, L.S. (1953). Stochastic Games, Proc. Nat. Acad. Sci. U.S.A. 39,1095–1100.
Warga, J. (1972). Optimal Control of Differential and Functional Equations, Academic Press, New York.
Whitt, W. (1980). Representation and Approximation of Noncooperative Sequential Games, SIAM J. Control Optim. 18, 33–48.
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© 1991 Springer Science+Business Media Dordrecht
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Nowak, A.S. (1991). Existence of Correlated Weak Equilibria in Discounted Stochastic Games with General State Space. In: Raghavan, T.E.S., Ferguson, T.S., Parthasarathy, T., Vrieze, O.J. (eds) Stochastic Games And Related Topics. Theory and Decision Library, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3760-7_12
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DOI: https://doi.org/10.1007/978-94-011-3760-7_12
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