Markov-perfect Nash equilibria in a class of resource games

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Markov-perfect Nash equilibria in a class of resource games

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Gerhard Sorger (Department of Economics, University of Vienna, BrØnner Str. 72, A-1210 Vienna, AUSTRIA)

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Gerhard Sorger

Abstract

A general model of non-cooperating agents exploiting a renewable resource is considered. Assuming that the resource is sufficiently productive we prove that there exists a continuum of Markov-perfect Nash equilibria (MPNE). Although these equilibria lead to over-exploitation one can approximate the efficient solution by MPNE both in the state space and the payoff space. Furthermore, we derive a necessary and sufficient condition for maximal exploitation of the resource to qualify as a MPNE. This condition is satisfied if there are sufficiently many players, or if the players are sufficiently impatient, or if the capacity of each player is sufficiently high.

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Article provided by Springer in its journal Economic Theory.

Volume (Year): 11 (1997)
Issue (Month): 1 ()
Pages: 79-100
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Handle: RePEc:spr:joecth:v:11:y:1997:i:1:p:79-100

Note: Received: November 1, 1996
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Paper
- Gerhard Sorger, 1996. "Markov Perfect Nash Equilibria in a Class of Resource Games," CIRANO Working Papers 96s-15, CIRANO. [Downloadable!]

References listed on IDEAS
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Benhabib, Jess & Radner, Roy, 1992. "The Joint Exploitation of a Productive Asset: A Game-Theoretic Approach," Economic Theory, Springer, vol. 2(2), pages 155-90, April.
Dutta, Prajit K & Sundaram, Rangarajan, 1992. "Markovian Equilibrium in a Class of Stochastic Games: Existence Theorems for Discounted and Undiscounted Models," Economic Theory, Springer, vol. 2(2), pages 197-214, April.
Benhabib, Jess & Radner, Roy, 1988. "Joint Exploitation Of A Productive Asset: A Game-Theoretic Approach," Working Papers 88-17, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
Reinganum, Jennifer F & Stokey, Nancy L, 1985. "Oligopoly Extraction of a Common Property Natural Resource: The Importance of the Period of Commitment in Dynamic Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 161-73, February. [Downloadable!] (restricted)
Dockner, Engelbert J. & Sorger, Gerhard, 1996. "Existence and Properties of Equilibria for a Dynamic Game on Productive Assets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 209-227, October. [Downloadable!] (restricted)
Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-39, May. [Downloadable!] (restricted)

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