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Existence of Nash equilibria in stochastic games of resource extraction with risk-sensitive players

Author

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  • Hubert Asienkiewicz

    (University of Zielona Góra)

  • Łukasz Balbus

    (University of Zielona Góra)

Abstract

We consider a two-person stochastic game of resource extraction. It is assumed that players have identical preferences. A novelty relies on the fact that each player is equipped with the same risk coefficient and calculates his discounted utility in the infinite time horizon in a recursive way by applying the entropic risk measure parametrized by this risk coefficient. Under two alternative sets of assumptions, we prove the existence of a symmetric stationary Markov perfect equilibrium.

Suggested Citation

  • Hubert Asienkiewicz & Łukasz Balbus, 2019. "Existence of Nash equilibria in stochastic games of resource extraction with risk-sensitive players," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 502-518, October.
    • Handle: RePEc:spr:topjnl:v:27:y:2019:i:3:d:10.1007_s11750-019-00516-2
    DOI: 10.1007/s11750-019-00516-2
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    References listed on IDEAS

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    1. Piotr Szajowski, 2006. "Constructions of Nash Equilibria in Stochastic Games of Resource Extraction with Additive Transition Structure," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 239-260, May.
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    7. Łukasz Balbus & Andrzej S. Nowak, 2004. "Construction of Nash equilibria in symmetric stochastic games of capital accumulation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 267-277, October.
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    13. Łukasz Balbus & Anna Jaśkiewicz & Andrzej S. Nowak, 2015. "Existence of Stationary Markov Perfect Equilibria in Stochastic Altruistic Growth Economies," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 295-315, April.
    14. Anderson, Evan W., 2005. "The dynamics of risk-sensitive allocations," Journal of Economic Theory, Elsevier, vol. 125(2), pages 93-150, December.
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