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Markov Perfect Nash Equilibria in a Class of Resource Games

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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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  • Gerhard Sorger, 1996. "Markov Perfect Nash Equilibria in a Class of Resource Games," CIRANO Working Papers 96s-15, CIRANO.
    • Handle: RePEc:cir:cirwor:96s-15
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    File URL: https://cirano.qc.ca/files/publications/96s-15.pdf
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Rodrigo Harrison & Roger Lagunoff, 2015. "Tipping Points and Business-as-Usual in a Global Carbon Commons," Working Papers gueconwpa~15-15-01, Georgetown University, Department of Economics, revised 12 Jul 2015.
    2. Bård Harstad, 2016. "The Dynamics Of Climate Agreements," Journal of the European Economic Association, European Economic Association, vol. 14(3), pages 719-752, June.
    3. Antoniadou, Elena & Koulovatianos, Christos & Mirman, Leonard J., 2013. "Strategic exploitation of a common-property resource under uncertainty," Journal of Environmental Economics and Management, Elsevier, vol. 65(1), pages 28-39.
    4. Salvador Ortigueira, 2004. "Markovian Optimal Taxation," Computing in Economics and Finance 2004 10, Society for Computational Economics.
    5. 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.
    6. Colin Rowat & Jayasri Dutta, 2007. "The Commons with Capital Markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 225-254, May.
    7. Jayasri Dutta & Colin Rowat, 2004. "The Road to Extinction: Commons with Capital Markets," Discussion Papers 04-11, Department of Economics, University of Birmingham, revised Jan 2007.
    8. Harrison, Rodrigo & Lagunoff, Roger, 2019. "Tipping points and business-as-usual in a global commons," Journal of Economic Behavior & Organization, Elsevier, vol. 163(C), pages 386-408.
    9. Josa-Fombellida, Ricardo & Rincón-Zapatero, Juan Pablo, 2008. "Markov Perfect Nash Equilibrium in stochastic differential games as solution of a generalized Euler Equations System," UC3M Working papers. Economics we086731, Universidad Carlos III de Madrid. Departamento de Economía.
    10. Ken-Ichi Akao, 2008. "Tax schemes in a class of differential games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 155-174, April.
    11. Jayasri Dutta & Colin Rowat, 2004. "The Road to Extinction: Commons with Capital Markets," GE, Growth, Math methods 0412001, University Library of Munich, Germany.
    12. 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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