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Best response dynamics for role games

Author

Listed:
  • Ulrich Berger

    (Vienna University of Economics, Department VW5, Augasse 2-6, A-1090 Vienna, Austria)

Abstract

In a role game, players can condition their strategies on their player position in the base game. If the base game is strategically equivalent to a zero-sum game, the set of Nash equilibria of the role game is globally asymptotically stable under the best response dynamics. If the base game is 2 ×2, then in the cyclic case the set of role game equilibria is a continuum. We identify a single equilibrium in this continuum that attracts all best response paths outside the continuum.

Suggested Citation

  • Ulrich Berger, 2002. "Best response dynamics for role games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 527-538.
    • Handle: RePEc:spr:jogath:v:30:y:2002:i:4:p:527-538
    Note: Received: June 2001
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    Citations

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    Cited by:

    1. Ulrich Berger, 2012. "Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play," Dynamic Games and Applications, Springer, vol. 2(1), pages 4-17, March.
    2. Ulrich Berger, 2003. "Continuous Fictitious Play via Projective Geometry," Game Theory and Information 0303004, University Library of Munich, Germany.
    3. Gorodeisky, Ziv, 2009. "Deterministic approximation of best-response dynamics for the Matching Pennies game," Games and Economic Behavior, Elsevier, vol. 66(1), pages 191-201, May.
    4. Luciano Andreozzi, 2010. "Trust is bound to emerge (In the repeated Trust Game)," Department of Economics Working Papers 1008, Department of Economics, University of Trento, Italia.
    5. Ulrich Berger, 2016. "Learning to trust, learning to be trustworthy," Department of Economics Working Papers wuwp212, Vienna University of Economics and Business, Department of Economics.
    6. Sawa, Ryoji & Zusai, Dai, 2014. "Evolutionary imitative dynamics with population-varying aspiration levels," Journal of Economic Theory, Elsevier, vol. 154(C), pages 562-577.
    7. Ulrich Berger, 2003. "A general model of best response adaptation," Game Theory and Information 0303008, University Library of Munich, Germany.
    8. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    9. W. C. Abram & K. Noray, 2018. "Political Corruption and Public Activism: An Evolutionary Game-Theoretic Analysis," Dynamic Games and Applications, Springer, vol. 8(1), pages 1-21, March.
    10. Andreozzi, Luciano, 2013. "Evolutionary stability in repeated extensive games played by finite automata," Games and Economic Behavior, Elsevier, vol. 79(C), pages 67-74.

    More about this item

    Keywords

    Role Games · Best Response Dynamics · Learning · Evolution.;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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