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On stochastic games in economics

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  • Andrzej Nowak

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Abstract

In this paper we show that many results on equilibria in stochastic games arising from economic theory can be deduced from the theorem on the existence of a correlated equilibrium due to Nowak and Raghavan. Some new classes of nonzero-sum Borel state space discounted stochastic games having stationary Nash equilibria are also presented. Three nontrivial examples of dynamic stochastic games arising from economic theory are given closed form solutions. Copyright Springer-Verlag 2007

Suggested Citation

  • Andrzej Nowak, 2007. "On stochastic games in economics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 513-530, December.
  • Handle: RePEc:spr:mathme:v:66:y:2007:i:3:p:513-530
    DOI: 10.1007/s00186-007-0167-8
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    References listed on IDEAS

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    1. Chakrabarti, Subir K., 1999. "Markov Equilibria in Discounted Stochastic Games," Journal of Economic Theory, Elsevier, vol. 85(2), pages 294-327, April.
    2. Diamond, Peter A, 1982. "Aggregate Demand Management in Search Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 90(5), pages 881-894, October.
    3. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    4. Dutta, Prajit K & Sundaram, Rangarajan, 1992. "Markovian Equilibrium in a Class of Stochastic Games: Existence Theorems for Discounted and Undiscounted Models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 197-214, April.
    5. Andrzej S. Nowak & Anna Jaśkiewicz, 2005. "Nonzero-sum semi-Markov games with the expected average payoffs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(1), pages 23-40, September.
    6. Horst, Ulrich, 2005. "Stationary equilibria in discounted stochastic games with weakly interacting players," Games and Economic Behavior, Elsevier, vol. 51(1), pages 83-108, April.
    7. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    8. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    9. 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.
    10. Andrzej Nowak, 2003. "On a new class of nonzero-sum discounted stochastic games having stationary Nash equilibrium points," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 121-132, December.
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    Citations

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    Cited by:

    1. Page, Frank, 2016. "Stationary Markov equilibria for approximable discounted stochastic games," LSE Research Online Documents on Economics 67808, London School of Economics and Political Science, LSE Library.
    2. John Duggan, 2011. "Noisy Stochastic Games," RCER Working Papers 562, University of Rochester - Center for Economic Research (RCER).
    3. Page, Frank, 2016. "On K-Class discounted stochastic games," LSE Research Online Documents on Economics 67809, London School of Economics and Political Science, LSE Library.
    4. Mitri Kitti, 2011. "Conditionally Stationary Equilibria in Discounted Dynamic Games," Dynamic Games and Applications, Springer, vol. 1(4), pages 514-533, December.
    5. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov-perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243.
    6. Frank H. Page, Jr. & Myrna H. Wooders, 2009. "Endogenous Network Dynamics," Caepr Working Papers 2009-002, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    7. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
    8. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
    9. John Duggan, 2012. "Noisy Stochastic Games," RCER Working Papers 570, University of Rochester - Center for Economic Research (RCER).
    10. Page, Frank, 2015. "Stationary Markov equilibria for K-class discounted stochastic games," LSE Research Online Documents on Economics 65103, London School of Economics and Political Science, LSE Library.
    11. Jaśkiewicz, Anna & Nowak, Andrzej S., 2014. "Stationary Markov perfect equilibria in risk sensitive stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 151(C), pages 411-447.
    12. Wenzhao Zhang & Yonghui Huang & Xianping Guo, 2014. "Nonzero-sum constrained discrete-time Markov games: the case of unbounded costs," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1074-1102, October.
    13. repec:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0194-2 is not listed on IDEAS
    14. Sachin Adlakha & Ramesh Johari, 2013. "Mean Field Equilibrium in Dynamic Games with Strategic Complementarities," Operations Research, INFORMS, vol. 61(4), pages 971-989, August.
    15. repec:eee:jetheo:v:169:y:2017:i:c:p:35-61 is not listed on IDEAS
    16. Łukasz Balbus & Łukasz Woźny, 2016. "A Strategic Dynamic Programming Method for Studying Short-Memory Equilibria of Stochastic Games with Uncountable Number of States," Dynamic Games and Applications, Springer, vol. 6(2), pages 187-208, June.
    17. 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.
    18. repec:spr:joptap:v:144:y:2010:i:1:d:10.1007_s10957-009-9588-2 is not listed on IDEAS
    19. 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.

    More about this item

    Keywords

    C73; E23; Stochastic games; Stationary equilibria; Supermodular games; Games with complementarities;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production

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