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Constructions of Nash Equilibria in Stochastic Games of Resource Extraction with Additive Transition Structure

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  • Piotr Szajowski

Abstract

A class of N-person stochastic games of resource extraction with discounted payoffs in discrete time is considered. It is assumed that transition probabilities have special additive structure. It is shown that the Nash equilibria and corresponding payoffs in finite horizon games converge as horizon goes to infinity. This implies existence of stationary Nash equilibria in the infinite horizon case. In addition the algorithm for finding Nash equilibria in infinite horizon games is discussed Copyright Springer-Verlag 2006

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  • 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.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:2:p:239-260
    DOI: 10.1007/s00186-005-0015-7
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    1. AMIR, Rabah, 2001. "Stochastic games in economics: the lattice-theoretic approach," LIDAM Discussion Papers CORE 2001059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    3. 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.
    4. Łukasz Balbus & Andrzej S. Nowak, 2004. "Construction of Nash equilibria in symmetric stochastic games of capital accumulation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 267-277, October.
    5. 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).
    6. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    7. 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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