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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)

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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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-39, May.
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Cited by:
  1. Jayasri Dutta & Colin Rowat, 2007. "The Road to Extinction: Commons with Capital Markets," WEF Working Papers 0024, ESRC World Economy and Finance Research Programme, Birkbeck, University of London.
  2. Salvador Ortigueira, 2004. "Markovian Optimal Taxation," 2004 Meeting Papers 315, Society for Economic Dynamics.
  3. Colin Rowat and Jayasri Dutta, 2004. "The commons with capital markets," Discussion Papers 05-01, Department of Economics, University of Birmingham.
  4. Ken-Ichi Akao, 2008. "Tax schemes in a class of differential games," Economic Theory, Springer, vol. 35(1), pages 155-174, April.
  5. Bård Harstad, 2010. "The Dynamics of Climate Agreements," CESifo Working Paper Series 2962, CESifo Group Munich.
  6. Salvador Ortigueira, 2006. "Markov-Perfect Optimal Taxation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(1), pages 153-178, January.
  7. Y. Hossein Farzin & Ken-Ichi Akao, 2006. "When is it Optimal to Exhaust a Resource in a Finite Time?," Working Papers 2006.23, Fondazione Eni Enrico Mattei.
  8. Ricardo Josa-Fombellida & Juan Pablo Rincón-Zapatero, 2008. "Markov Perfect Nash Equilibrium in stochastic differential games as solution of a generalized Euler Equations System," Economics Working Papers we086731, Universidad Carlos III, Departamento de Economía.
  9. Christos Koulovatianos & Elena Antoniadou & Leonard J.Mirman, 2007. "Strategic Exploitation of a Common-Property Resource under Uncertainty," Vienna Economics Papers 0703, University of Vienna, Department of Economics.

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