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Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games

Author

Listed:
  • Beatris Escobedo-Trujillo

    (CINVESTAV-IPN)

  • Daniel López-Barrientos

    (CINVESTAV-IPN)

  • Onésimo Hernández-Lerma

    (CINVESTAV-IPN)

Abstract

This paper deals with zero-sum stochastic differential games with long-run average payoffs. Our main objective is to give conditions for existence and characterization of bias and overtaking optimal equilibria. To this end, first we characterize the family of optimal average payoff strategies. Then, within this family, we impose suitable conditions to determine the subfamilies of bias and overtaking equilibria. A key step to obtain these facts is to show the existence of solutions to the average payoff optimality equations. This is done by the usual “vanishing discount” approach. Finally, a zero-sum game associated to a certain manufacturing process illustrates our results.

Suggested Citation

  • Beatris Escobedo-Trujillo & Daniel López-Barrientos & Onésimo Hernández-Lerma, 2012. "Bias and Overtaking Equilibria for Zero-Sum Stochastic Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 662-687, June.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:3:d:10.1007_s10957-011-9974-4
    DOI: 10.1007/s10957-011-9974-4
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    References listed on IDEAS

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    1. Nowak, Andrzej S., 2008. "Equilibrium in a dynamic game of capital accumulation with the overtaking criterion," Economics Letters, Elsevier, vol. 99(2), pages 233-237, May.
    2. Tomás Prieto-Rumeau & Onésimo Hernández-Lerma, 2005. "Bias and overtaking equilibria for zero-sum continuous-time Markov games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 437-454, July.
    3. Andrzej S. Nowak, 1999. "Sensitive equilibria for ergodic stochastic games with countable state spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(1), pages 65-76, August.
    4. Andrzej S. Nowak, 1999. "Optimal strategies in a class of zero-sum ergodic stochastic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 399-419, December.
    5. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
    6. Hiroshi Atsumi, 1965. "Neoclassical Growth and the Efficient Program of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 127-136.
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