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Stochastic Stability in Three-Player Games with Time Delays

Author

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  • Jacek Miȩkisz
  • Michał Matuszak
  • Jan Poleszczuk

Abstract

We discuss combined effects of stochasticity and time delays in finite-population three-player games with two mixed Nash equilibria and a pure one. We show that if basins of attraction of the stable interior equilibrium and the stable pure one are equal, then an arbitrary small time delay makes the pure one stochastically stable. Moreover, if the basin of attraction of the interior equilibrium is bigger than the one of the pure equilibrium, then there exists a critical time delay where the pure equilibrium becomes stochastically stable. Copyright The Author(s) 2014

Suggested Citation

  • Jacek Miȩkisz & Michał Matuszak & Jan Poleszczuk, 2014. "Stochastic Stability in Three-Player Games with Time Delays," Dynamic Games and Applications, Springer, vol. 4(4), pages 489-498, December.
    • Handle: RePEc:spr:dyngam:v:4:y:2014:i:4:p:489-498
    DOI: 10.1007/s13235-014-0115-1
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    References listed on IDEAS

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    1. Iijima, Ryota, 2011. "Heterogeneous information lags and evolutionary stability," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 83-85, March.
    2. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, vol. 70(1), pages 65-92, July.
    3. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, April.
    4. Hiroshi Oaku, 2002. "Evolution with Delay," The Japanese Economic Review, Japanese Economic Association, vol. 53(1), pages 114-133, March.
    5. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    6. Vega-Redondo, Fernando (ed.), 1996. "Evolution, Games, and Economic Behaviour," OUP Catalogue, Oxford University Press, number 9780198774723.
    7. Maciej Bukowski & Jacek Miekisz, 2004. "Evolutionary and asymptotic stability in symmetric multi-player games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 41-54, January.
    8. Kim, Youngse, 1996. "Equilibrium Selection inn-Person Coordination Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 203-227, August.
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    Cited by:

    1. Pan, Yanchun & Yang, Wen & Ma, Nan & Chen, Zhimin & Zhou, Ming & Xiong, Yi, 2019. "Game analysis of carbon emission verification: A case study from Shenzhen's cap-and-trade system in China," Energy Policy, Elsevier, vol. 130(C), pages 418-428.
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    3. Marek Bodnar & Jacek Miȩkisz & Raffi Vardanyan, 2020. "Three-Player Games with Strategy-Dependent Time Delays," Dynamic Games and Applications, Springer, vol. 10(3), pages 664-675, September.

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