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A Differential Game Approach To Evolutionary Equilibrium Selection

Author

Listed:
  • JOSEF HOFBAUER

    (Department of Mathematics, University of Vienna, Strudlhofgasse 4, A–1090 Wien, Austria)

  • GERHARD SORGER

    (Department of Economics, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK)

Abstract

The equilibrium selection model of Matsui and Matsuyama (1995), which is based on rational players who maximise their discounted future payoff, is analysed with the help of an associated differential game. Equilibrium selection results are derived for games with a ½-dominant equilibrium, for games with a potential function, and some simple supermodular games.

Suggested Citation

  • Josef Hofbauer & Gerhard Sorger, 2002. "A Differential Game Approach To Evolutionary Equilibrium Selection," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 17-31.
    • Handle: RePEc:wsi:igtrxx:v:04:y:2002:i:01:n:s0219198902000525
    DOI: 10.1142/S0219198902000525
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    Citations

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    Cited by:

    1. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
    2. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
    3. repec:ebl:ecbull:v:3:y:2007:i:19:p:1-8 is not listed on IDEAS
    4. , & , & ,, 2008. "Monotone methods for equilibrium selection under perfect foresight dynamics," Theoretical Economics, Econometric Society, vol. 3(2), June.
    5. Oyama, Daisuke, 2009. "History versus expectations in economic geography reconsidered," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 394-408, February.
    6. Matsui, Akihiko & Oyama, Daisuke, 2006. "Rationalizable foresight dynamics," Games and Economic Behavior, Elsevier, vol. 56(2), pages 299-322, August.
    7. Oyama, Daisuke, 2009. "Agglomeration under forward-looking expectations: Potentials and global stability," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 696-713, November.
    8. George Loginov, 2022. "Cyclical behavior of evolutionary dynamics in coordination games with changing payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 1-27, March.
    9. Kojima, Fuhito, 2006. "Risk-dominance and perfect foresight dynamics in N-player games," Journal of Economic Theory, Elsevier, vol. 128(1), pages 255-273, May.
    10. , & , & ,, 2008. "Monotone methods for equilibrium selection under perfect foresight dynamics," Theoretical Economics, Econometric Society, vol. 3(2), June.
    11. Carlos Alós-Ferrer & Nick Netzer, 2015. "Robust stochastic stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 31-57, January.
    12. Cao, Zhigang & Yang, Xiaoguang, 2018. "Symmetric games revisited," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 9-18.
    13. Hiroshi Uno, 2007. "Nested Potential Games," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-8.
    14. Yusuke Hino, 2011. "An improved algorithm for detecting potential games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 199-205, February.
    15. Kojima, Fuhito & Takahashi, Satoru, 2008. "p-Dominance and perfect foresight dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 689-701, September.
    16. Oyama, Daisuke, 2002. "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory, Elsevier, vol. 107(2), pages 288-310, December.
    17. Dirk Helbing & Anders Johansson, 2010. "Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach," PLOS ONE, Public Library of Science, vol. 5(10), pages 1-15, October.
    18. Daisuke Oyama & Satoru Takahashi, 2009. "Monotone and local potential maximizers in symmetric 3x3 supermodular games," Economics Bulletin, AccessEcon, vol. 29(3), pages 2123-2135.
    19. Lester T. Chan, 2021. "Divide and conquer in two‐sided markets: A potential‐game approach," RAND Journal of Economics, RAND Corporation, vol. 52(4), pages 839-858, December.
    20. Daisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2011. "Perfect foresight dynamics in binary supermodular games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(3), pages 251-267, September.
    21. Honda, Jun, 2011. "Noise-independent selection in global games and monotone potential maximizer: A symmetric 3×3 example," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 663-669.
    22. Iijima, Ryota, 2015. "Iterated generalized half-dominance and global game selection," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 120-136.
    23. Takaaki Abe & Satoshi Nakada, 2018. "Generalized Potentials, Value, and Core," Discussion Paper Series DP2018-19, Research Institute for Economics & Business Administration, Kobe University.

    More about this item

    Keywords

    Equilibrium Selection; Perfect Foresight; Potential Game; Supermodular Game; Pontryagin Maximum Principle;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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