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Lattice Methods in Computation of Sequential Markov Equilibrium in Dynamic Games

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Abstract

This paper uses lattice programming methods along with the extension of Tarski's fixed point theorem due to Veinott (1992) and Zhou (1994) to establish sufficient conditions for existence of sequential symmetric Markov equilibrium in a large class of dynamic games. Our method is constructive and we provide specific algorithms for computing equilibrium. These results are applied to the classic fishwar game in the context of a finite horizon. JEL Classification: C62, C63, C73, D90

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  • Manjira Datta & Leonard Mirman & Olivier Morand & Kevin Reffett, "undated". "Lattice Methods in Computation of Sequential Markov Equilibrium in Dynamic Games," Working Papers 2179545, Department of Economics, W. P. Carey School of Business, Arizona State University.
    • Handle: RePEc:asu:wpaper:2179545
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    References listed on IDEAS

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    1. Manjira Datta & Leonard J. Mirman, 2000. "Dynamic Externalities and Policy Coordination," Review of International Economics, Wiley Blackwell, vol. 8(1), pages 44-59, February.
    2. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, September.
    3. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
    4. Datta, Manjira, 1997. "Externalities and Price Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 587-603, August.
    5. Datta, Manjira & Mirman, Leonard J., 1999. "Externalities, Market Power, and Resource Extraction," Journal of Environmental Economics and Management, Elsevier, vol. 37(3), pages 233-255, May.
    6. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    7. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    8. Sundaram, Rangarajan K., 1989. "Perfect equilibrium in non-randomized strategies in a class of symmetric dynamic games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 153-177, February.
    9. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    10. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    11. David Levhari & Leonard J. Mirman, 1980. "The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 322-334, Spring.
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    Cited by:

    1. Manjira Datta & Leonard Mirman & Kevin Reffett, "undated". "Nonclassical Brock-Mirman Economies," Working Papers 2179544, Department of Economics, W. P. Carey School of Business, Arizona State University.

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    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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