Stationary Markov Perfect Equilibria in Discounted Stochastic Games

He, Wei and Sun, Yeneng (2013): Stationary Markov Perfect Equilibria in Discounted Stochastic Games.

Abstract

The existence of stationary Markov perfect equilibria in stochastic games is shown in several contexts under a general condition called "coarser transition kernels". These results include various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with mixtures of constant transition kernels as special cases. The minimality of the condition is illustrated. The results here also shed some new light on a recent example on the nonexistence of stationary equilibrium. The proofs are remarkably simple via establishing a new connection between stochastic games and conditional expectations of correspondences.

• Item Type: MPRA Paper
• Language: English
• Keywords: Stochastic game, stationary Markov perfect equilibrium, equilibrium existence, coarser transition kernel
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

References

1. C. D. Aliprantis and K. C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, Springer, Berlin, 2006.

2. D. Duffie, Dynamic Asset Pricing Theory, 3rd edition, Princeton University Press, Princeton, 2001.

3. D. Duffie, J. Geanakoplos, A. Mas-Colell and A. McLennan, Stationary Markov Equilibria, Econometrica 62 (1994), 745-781.

4. J. Duggan, Noisy Stochastic Games, Econometrica 80 (2012), 2017-2045.

5. E. B. Dynkin and I. V. Evstigneev, Regular Conditional Expectations of Correspondences, Theory of Probability and its Applications 21 (1977), 325-338.

6. Y. Levy, A Discounted Stochastic Game with No Stationary Nash Equilibrium: Two Examples, Econometrica 81 (2013), 1973-2007.

7. A. S. Nowak, On a New Class of Nonzero-Sum Discounted Stochastic Games Having Stationary Nash Equilibrium Points, International Journal of Game Theory 32 (2003), 121-132.

8. A. S. Nowak and T. E. S. Raghavan, Existence of Stationary Correlated Equilibria with Symmetric Information for Discounted Stochastic Games, Mathematics of Operations Research 17 (1992), 519-527.

9. L. Shapley, Stochastic Games, Proceedings of the National Academy of Sciences USA 39 (1953), 1095-1100.