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Stochastic games in economics: the lattice-theoretic approach

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  • AMIR, Rabah

Abstract

This chapter considers a recent trend in the application of stochastic games to economics characterized by the use of the lattice-theoretic approach to capture the monotonic properties of Markovian equilibria. The topics covered are: (i) a general framework for discounted stochastic games with Liptchitz-continuous and monotone equilibrium strategies and values, (ii) a model of capital accumulation, (iii) two classes of games with perfect information, in strategic bequests and oligopoly with commitment. In view of the restriction to pure-strategy equilibria and of the natural monotonicity property of strategies and value functions in most economic applications, this approach appears most promising.
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Suggested Citation

  • AMIR, Rabah, 2003. "Stochastic games in economics: the lattice-theoretic approach," LIDAM Reprints CORE 1663, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:1663
    DOI: 10.1007/978-94-010-0189-2_29
    Note: In : A. Neyman and S. Sorin (eds.), Stochastic Games and Applications. Dordrecht, Kluwer Academic Publishers, 443-453, 2003
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    References listed on IDEAS

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    1. Amir, Rabah, 1996. "Strategic Intergenerational Bequests with Stochastic Convex Production," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 367-376, August.
    2. Wolfgang Leininger, 1986. "The Existence of Perfect Equilibria in a Model of Growth with Altruism between Generations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(3), pages 349-367.
    3. Rabah Amir, 2002. "Complementarity and Diagonal Dominance in Discounted Stochastic Games," Annals of Operations Research, Springer, vol. 114(1), pages 39-56, August.
    4. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    5. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    6. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    7. B. Douglas Bernheim & Debraj Ray, 1987. "Economic Growth with Intergenerational Altruism," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(2), pages 227-243.
    8. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    9. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    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. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, I: Overview and Quantity Competition with Large Fixed Costs," Econometrica, Econometric Society, vol. 56(3), pages 549-569, May.
    12. Frieda Granot & Arthur F. Veinott, 1985. "Substitutes, Complements and Ripples in Network Flows," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 471-497, August.
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    Cited by:

    1. 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.
    2. Elena M. Parilina & Alessandro Tampieri, 2018. "Stability and cooperative solution in stochastic games," Theory and Decision, Springer, vol. 84(4), pages 601-625, June.
    3. AMIR, Rabah, 2001. "Stochastic games in economics and related fields: an overview," LIDAM Discussion Papers CORE 2001060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. repec:luc:wpaper:16-22 is not listed on IDEAS
    5. Akihiko Yanase, 2005. "Pollution Control in Open Economies: Implications of Within-period Interactions for Dynamic Game Equilibrium," Journal of Economics, Springer, vol. 84(3), pages 277-311, May.
    6. Laussel, Didier & Resende, Joana, 2014. "Dynamic price competition in aftermarkets with network effects," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 106-118.

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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives

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