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The Instability of the Nash Equilibrium in Common-Pool Resources

Author

Listed:
  • Tatsuyoshi Saijo

    (Kochi University of Technology)

  • Yutaka Kobayashi

    (Kochi University of Technology)

Abstract

Efficient allocations in common-pool resources cannot be accomplished when appropriators are selfish. In addition to this dilemma, using a linear approximation of best response functions at the Nash equilibrium in the common-pool resource environment, we find that the system of simultaneous difference equations is locally unstable if the number of appropriators is at least four. This result indicates that the equilibrium analysis might not capture the essence of the common-pool resource problem, but provides an answer to ``some unexplained pulsing behavior'' (Ostrom, Journal of Economic Behavior and Organization, vol. 61, no.2 [2006], p. 150) of each appropriator's labor input in common-pool resource experiments.

Suggested Citation

  • Tatsuyoshi Saijo & Yutaka Kobayashi, 2014. "The Instability of the Nash Equilibrium in Common-Pool Resources," Working Papers SDES-2014-5, Kochi University of Technology, School of Economics and Management, revised Oct 2014.
    • Handle: RePEc:kch:wpaper:sdes-2014-5
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    File URL: http://www.souken.kochi-tech.ac.jp/seido/wp/SDES-2014-5.pdf
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    References listed on IDEAS

    as
    1. Rodriguez-Sickert, Carlos & Guzmán, Ricardo Andrés & Cárdenas, Juan Camilo, 2008. "Institutions influence preferences: Evidence from a common pool resource experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 215-227, July.
    2. Ito, Masaru & Saijo, Tatsuyoshi & Une, Masashi, 1995. "The Tragedy of the Commons revisited Identifying behavioral principles," Journal of Economic Behavior & Organization, Elsevier, vol. 28(3), pages 311-335, December.
    3. Walker, James M & Gardner, Roy, 1992. "Probabilistic Destruction of Common-Pool Resources: Experimental Evidence," Economic Journal, Royal Economic Society, vol. 102(414), pages 1149-1161, September.
    4. Ostrom, Elinor, 2006. "The value-added of laboratory experiments for the study of institutions and common-pool resources," Journal of Economic Behavior & Organization, Elsevier, vol. 61(2), pages 149-163, October.
    5. Hayo, Bernd & Vollan, Björn, 2012. "Group interaction, heterogeneity, rules, and co-operative behaviour: Evidence from a common-pool resource experiment in South Africa and Namibia," Journal of Economic Behavior & Organization, Elsevier, vol. 81(1), pages 9-28.
    6. Walker, James M. & Gardner, Roy & Ostrom, Elinor, 1990. "Rent dissipation in a limited-access common-pool resource: Experimental evidence," Journal of Environmental Economics and Management, Elsevier, vol. 19(3), pages 203-211, November.
    7. Casari, Marco & Plott, Charles R., 2003. "Decentralized management of common property resources: experiments with a centuries-old institution," Journal of Economic Behavior & Organization, Elsevier, vol. 51(2), pages 217-247, June.
    8. Timothy Cason & Lata Gangadharan, 2015. "Promoting cooperation in nonlinear social dilemmas through peer punishment," Experimental Economics, Springer;Economic Science Association, vol. 18(1), pages 66-88, March.
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    Cited by:

    1. Tatsuyoshi Saijo, 2014. "The instability of the voluntary contribution mechanism," Working Papers SDES-2014-3, Kochi University of Technology, School of Economics and Management, revised Oct 2014.

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    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery

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