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Markov Perfect Nash Equilibria in a Class of Resource Games

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  • Gerhard Sorger

Abstract

A standard model of the exploitation of a renewable resource by non-cooperating agents is considered. Under the assumption that the resource is sufficiently productive we prove that there exist infinitely many Markov-perfect Nash equilibria (MPNE). Although these equilibria lead to overexploitation of the resource (tragedy of the commons) it is shown that for any T > 0 there exist MPNE with the property that the resource stock stays in an arbitrary small neighborhood of the efficient steady state for at least T time periods. Furthermore, we derive a necessary and sufficient condition for maximal exploitation of the resource to qualify as a MPNE and show that 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. On analyse un modèle standard de l'exploitation des ressources renouvelables par des agents non-coopératifs. Dans le cas où les ressources sont suffisamment productives, on démontre l'existence d'un continuum d'équilibres Markov-parfaits de Nasch (EMPN). Quoique ces équilibres entrainent la surconsommation des ressources, on peut prouver que pour chaque T > 0, il y a des EMPN ayant la propriété que le stock de ressources demeure dans un voisinage arbitrairement petit de l'état stationnaire optimal pendant au moins T périodes. De plus, on obtient une condition nécessaire et suffisante pour que l'exploitation maximale des ressources soit un EMPN. On démontre que cette condition est vérifiée dans le cas où soit il y a beaucoup d'agents, soit les agents sont impatients, soit la capacité de chaque agent est grande.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 96s-15.

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Date of creation: 01 Apr 1996
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Handle: RePEc:cir:cirwor:96s-15

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Keywords: Renewable resources; differential game; Markov perfect equilibria; multiple equilibria; Ressources renouvelables; jeu différentiel; équilibres Markov-parfaits; équilibres multiples;

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References

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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. 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.
  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, vol. 2(2), pages 197-214, April.
  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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Citations

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Cited by:
  1. 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.
  2. Jayasri Dutta & Colin Rowat, 2004. "The Road to Extinction: Commons with Capital Markets," GE, Growth, Math methods 0412001, EconWPA.
  3. Colin Rowat and Jayasri Dutta, 2005. "The Commons with Capital Markets," Discussion Papers 05-19, Department of Economics, University of Birmingham.
  4. Salvador Ortigueira, 2004. "Markovian Optimal Taxation," Computing in Economics and Finance 2004 10, Society for Computational Economics.
  5. Ken-Ichi Akao, 2008. "Tax schemes in a class of differential games," Economic Theory, Springer, vol. 35(1), pages 155-174, April.
  6. 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.
  7. Bard Harstad, 2009. "The Dynamics of Climate Agreements," Discussion Papers 1474, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. 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.
  9. 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.

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