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Stationary Markov Perfect Equilibria in Discounted Stochastic Games

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  • Wei He
  • Yeneng Sun

Abstract

The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result covers various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with finite actions and state-independent transitions, and stochastic games with mixtures of constant transition kernels as special cases. A remarkably simple proof is provided via establishing a new connection between stochastic games and conditional expectations of correspondences. New applications of stochastic games are presented as illustrative examples, including stochastic games with endogenous shocks and a stochastic dynamic oligopoly model.

Suggested Citation

  • Wei He & Yeneng Sun, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," Papers 1311.1562, arXiv.org, revised Jan 2017.
    • Handle: RePEc:arx:papers:1311.1562
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    References listed on IDEAS

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    1. John Duggan, 2012. "Noisy Stochastic Games," Econometrica, Econometric Society, vol. 80(5), pages 2017-2045, September.
    2. Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Nash Equilibrium," Discussion Paper Series dp596r, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised May 2012.
    3. John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).
    4. Yehuda Levy, 2013. "Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples," Econometrica, Econometric Society, vol. 81(5), pages 1973-2007, September.
    5. A. S. Nowak & T. E. S. Raghavan, 1992. "Existence of Stationary Correlated Equilibria with Symmetric Information for Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 519-526, August.
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    Cited by:

    1. Fu, Jing & Page, Frank & Zigrand, Jean-Pierre, 2022. "Layered networks, equilibrium dynamics, and stable coalitions," LSE Research Online Documents on Economics 118874, London School of Economics and Political Science, LSE Library.
    2. Wei He, 2022. "Discontinuous stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 827-858, June.
    3. Damián Pierri, 2023. "Simulations in Models with Heterogeneous Agents, Incomplete Markets and Aggregate Uncertainty," Working Papers 259, Red Nacional de Investigadores en Economía (RedNIE).
    4. Wei He & Yeneng Sun, 2018. "Conditional expectation of correspondences and economic applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 265-299, August.
    5. Hülya Eraslan & Kirill S. Evdokimov & Jan Zápal, 2022. "Dynamic Legislative Bargaining," Springer Books, in: Emin Karagözoğlu & Kyle B. Hyndman (ed.), Bargaining, chapter 0, pages 151-175, Springer.
    6. David González-Sánchez & Fernando Luque-Vásquez & J. Adolfo Minjárez-Sosa, 2019. "Zero-Sum Markov Games with Random State-Actions-Dependent Discount Factors: Existence of Optimal Strategies," Dynamic Games and Applications, Springer, vol. 9(1), pages 103-121, March.
    7. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    8. Subir K. Chakrabarti, 2021. "Stationary equilibrium in stochastic dynamic models: Semi-Markov strategies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 177-194, October.
    9. Fu, Jing & Page, Frank, 2022. "Discounted stochastic games, the 3M property and stationary Markov perfect equilibria," LSE Research Online Documents on Economics 118865, London School of Economics and Political Science, LSE Library.
    10. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    11. Jing Fu & Frank Page & Jean-Pierre Zigrand, 2023. "Correction to: Layered Networks, Equilibrium Dynamics, and Stable Coalitions," Dynamic Games and Applications, Springer, vol. 13(2), pages 669-704, June.
    12. Jenkins, Mark & Liu, Paul & Matzkin, Rosa L. & McFadden, Daniel L., 2021. "The browser war — Analysis of Markov Perfect Equilibrium in markets with dynamic demand effects," Journal of Econometrics, Elsevier, vol. 222(1), pages 244-260.
    13. Dang, Chuangyin & Herings, P. Jean-Jacques & Li, Peixuan, 2020. "An Interior-Point Path-Following Method to Compute Stationary Equilibria in Stochastic Games," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
    14. He, Wei & Sun, Yeneng, 2020. "Dynamic games with (almost) perfect information," Theoretical Economics, Econometric Society, vol. 15(2), May.
    15. Anna Jaśkiewicz & Andrzej S. Nowak, 2021. "Markov decision processes with quasi-hyperbolic discounting," Finance and Stochastics, Springer, vol. 25(2), pages 189-229, April.
    16. Jie Ning, 2021. "Reducible Markov Decision Processes and Stochastic Games," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2726-2751, August.
    17. Chuangyin Dang & P. Jean-Jacques Herings & Peixuan Li, 2022. "An Interior-Point Differentiable Path-Following Method to Compute Stationary Equilibria in Stochastic Games," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1403-1418, May.
    18. Jing Fu & Frank Page & Jean-Pierre Zigrand, 2023. "Layered Networks, Equilibrium Dynamics, and Stable Coalitions," Dynamic Games and Applications, Springer, vol. 13(2), pages 636-668, June.

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