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Stationary equilibrium in stochastic dynamic models: Semi-Markov strategies

Author

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  • Subir K. Chakrabarti

    (Indiana University Purdue University Indianapolis(IUPUI))

Abstract

We show here that a stationary equilibrium in Semi-Markov strategies exists for stochastic games under just the condition of norm continuity of the transition probability that are absolutely continuous with respect to a fixed measure on the state space. We also show that the result can be extended to the case of generalized games in which the feasible action correspondences depend on the action of the other players. We show that the generalization allows one to directly apply the results to general dynamic models.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:etbull:v:9:y:2021:i:2:d:10.1007_s40505-021-00202-2
    DOI: 10.1007/s40505-021-00202-2
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    References listed on IDEAS

    as
    1. Chakrabarti, Subir K., 1999. "Markov Equilibria in Discounted Stochastic Games," Journal of Economic Theory, Elsevier, vol. 85(2), pages 294-327, April.
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    4. Yehuda Levy, 2013. "Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples," Econometrica, Econometric Society, vol. 81(5), pages 1973-2007, September.
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    6. Yehuda John Levy & Andrew McLennan, 2015. "Corrigendum to “Discounted Stochastic Games With No Stationary Nash Equilibrium: Two Examples”," Econometrica, Econometric Society, vol. 83(3), pages 1237-1252, May.
    7. Barelli, Paulo & Duggan, John, 2014. "A note on semi-Markov perfect equilibria in discounted stochastic games," Journal of Economic Theory, Elsevier, vol. 151(C), pages 596-604.
    8. He, Wei & Sun, Yeneng, 2017. "Stationary Markov perfect equilibria in discounted stochastic games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 35-61.
    9. Anna Jaśkiewicz & Andrzej S. Nowak, 2016. "Stationary Almost Markov Perfect Equilibria in Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 430-441, May.
    10. Mertens, J.-F., 1987. "A measurable “measurable choice” theorem," LIDAM Discussion Papers CORE 1987049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).
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    More about this item

    Keywords

    Stochastic games; Markov perfect equilibrium; Semi-Markov strategies; Stationary Markov equilibrium; Subgame perfect equilibrium; Stationary semi-Markov perfect equilibrium; Almost Markov perfect equilibrium;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • 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
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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