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Stationary Markov perfect equilibria in discounted stochastic games

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  • He, Wei
  • Sun, Yeneng

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

  • He, Wei & Sun, Yeneng, 2017. "Stationary Markov perfect equilibria in discounted stochastic games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 35-61.
    • Handle: RePEc:eee:jetheo:v:169:y:2017:i:c:p:35-61
    DOI: 10.1016/j.jet.2017.01.007
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    2. 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.
    3. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    4. Anna Jaśkiewicz & Andrzej S. Nowak, 2021. "Markov decision processes with quasi-hyperbolic discounting," Finance and Stochastics, Springer, vol. 25(2), pages 189-229, April.
    5. 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.
    6. Damián Pierri, 2023. "Simulations in Models with Heterogeneous Agents, Incomplete Markets and Aggregate Uncertainty," Working Papers 259, Red Nacional de Investigadores en Economía (RedNIE).
    7. 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.
    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. 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.
    10. He, Wei & Sun, Yeneng, 2020. "Dynamic games with (almost) perfect information," Theoretical Economics, Econometric Society, vol. 15(2), May.
    11. Wei He, 2022. "Discontinuous stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 827-858, June.
    12. Cao, Dan, 2020. "Recursive equilibrium in Krusell and Smith (1998)," Journal of Economic Theory, Elsevier, vol. 186(C).
    13. Runjie Geng, 2018. "Recursive equilibria in dynamic economies withbounded rationality," 2018 Meeting Papers 137, Society for Economic Dynamics.
    14. 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.
    15. 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).
    16. 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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    More about this item

    Keywords

    Stochastic game; Stationary Markov perfect equilibrium; (Decomposable) coarser transition kernel; Endogenous shocks; Dynamic oligopoly;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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