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Markovian Equilibrium in a Class of Stochastic Games: Existence Theorems for Discounted and Undiscounted Models

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  • Dutta, Prajit K
  • Sundaram, Rangarajan

Abstract

We study a strategic version of the neoclassical growth model under possible production uncertainty. For a general specification of the problem, we establish (1) the existence of stationary Markov equilibria in pure strategies for the discounted game, and (2) the convergence, under a boundedness condition, of discounted equilibrium strategies to a pure strategy stationary Markovian equilibrium of the undiscounted game as the discount factor tends to unity. The same techniques can be used to prove that such convergence also obtains in all finite-state, finite-action stochastic games satisfying a certain "full communicability" condition. These results are of special interest since there are well known examples in the literature in which the limit of discounted.equilibria fails to be an equilibrium of the undiscounted game.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:2:y:1992:i:2:p:197-214
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    Cited by:

    1. Steinmetz, Alexander, 2010. "Price and inventory dynamics in an oligopoly industry: A framework for commodity markets," W.E.P. - Würzburg Economic Papers 82, University of Würzburg, Chair for Monetary Policy and International Economics.
    2. Janusz Matkowski & Andrzej Nowak, 2011. "On discounted dynamic programming with unbounded returns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 455-474, April.
    3. Antoniadou, Elena & Koulovatianos, Christos & Mirman, Leonard J., 2013. "Strategic exploitation of a common-property resource under uncertainty," Journal of Environmental Economics and Management, Elsevier, vol. 65(1), pages 28-39.
    4. Piotr Szajowski, 2006. "Constructions of Nash Equilibria in Stochastic Games of Resource Extraction with Additive Transition Structure," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 239-260, May.
    5. Gerhard Sorger, 1997. "Markov-perfect Nash equilibria in a class of resource games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 79-100.
    6. Mitri Kitti, 2011. "Conditionally Stationary Equilibria in Discounted Dynamic Games," Dynamic Games and Applications, Springer, vol. 1(4), pages 514-533, December.
    7. Christos Koulovatianos & Leonard J. Mirman, 2003. "R&D Investment, Market Structure, and Industry Growth," University of Cyprus Working Papers in Economics 8-2003, University of Cyprus Department of Economics.
    8. 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.
    9. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov-perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243.
    10. Steve Alpern & Shmuel Gal, 2009. "Analysis and design of selection committees: a game theoretic secretary problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 377-394, November.
    11. Christos Koulovatianos & Leonard J. Mirman, 2003. "The Effects of Market Structure on Industry Growth," University of Cyprus Working Papers in Economics 7-2003, University of Cyprus Department of Economics.
    12. Nowak, Andrzej S., 2008. "Equilibrium in a dynamic game of capital accumulation with the overtaking criterion," Economics Letters, Elsevier, vol. 99(2), pages 233-237, May.
    13. 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.
    14. Prajit Dutta & Roy Radner, 2012. "Capital growth in a global warming model: will China and India sign a climate treaty?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(2), pages 411-443, February.
    15. Dutta, Prajit K. & Radner, Roy, 2009. "A strategic analysis of global warming: Theory and some numbers," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 187-209, August.
    16. Koulovatianos, Christos & Mirman, Leonard J., 2007. "The effects of market structure on industry growth: Rivalrous non-excludable capital," Journal of Economic Theory, Elsevier, vol. 133(1), pages 199-218, March.
    17. 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.
    18. Tapan Mitra & Gerhard Sorger, 2015. "Noncooperative Resource Exploitation by Patient Players," Dynamic Games and Applications, Springer, vol. 5(3), pages 361-377, September.
    19. Khan, M. Ali, 2016. "On a forest as a commodity and on commodification in the discipline of forestry," Forest Policy and Economics, Elsevier, vol. 72(C), pages 7-17.
    20. Alexander Steinmetz, 2010. "Price and Inventory Dynamics in an Oligopoly Industry: A Framework for Commodity Markets," Working Papers 092, Bavarian Graduate Program in Economics (BGPE).
    21. Christos Koulovatianos, 2015. "Strategic Exploitation of a Common-Property Resource Under Rational Learning About its Reproduction," Dynamic Games and Applications, Springer, vol. 5(1), pages 94-119, March.
    22. Escobar, Juan F., 2013. "Equilibrium analysis of dynamic models of imperfect competition," International Journal of Industrial Organization, Elsevier, vol. 31(1), pages 92-101.
    23. Balbus, Łukasz & Jaśkiewicz, Anna & Nowak, Andrzej S., 2015. "Stochastic bequest games," Games and Economic Behavior, Elsevier, vol. 90(C), pages 247-256.

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