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Almost global convergence to p-dominant equilibrium

Author

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  • Sandholm,W.H.

    (University of Wisconsin-Madison, Social Systems Research Institute)

Abstract

A population of players repeatedly plays an n strategy symmetric game. Players update their strategies by sampling the behavior of k opponents and playing a best response to the distribution of strategies in the sample. Suppose the game possesses a ${1 \over k}$-dominant strategy which is initially played by a positive fraction of the population. Then if the population size is large enough, play converges to the ${1 \over k}$-dominant equilibrium with arbitrarily high probability.
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Suggested Citation

  • Sandholm,W.H., 1999. "Almost global convergence to p-dominant equilibrium," Working papers 37, Wisconsin Madison - Social Systems.
  • Handle: RePEc:att:wimass:199937
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    File URL: http://www.ssc.wisc.edu/~whs/research/gc.pdf
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    References listed on IDEAS

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    1. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, pages 145-157.
    2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    3. Saez-Marti, Maria & Weibull, Jorgen W., 1999. "Clever Agents in Young's Evolutionary Bargaining Model," Journal of Economic Theory, Elsevier, pages 268-279.
    4. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
    5. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    7. Kaniovski Yuri M. & Young H. Peyton, 1995. "Learning Dynamics in Games with Stochastic Perturbations," Games and Economic Behavior, Elsevier, vol. 11(2), pages 330-363, November.
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    Citations

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    Cited by:

    1. Abi Adams & Laurens Cherchye & Bram De Rock & Ewout Verriest, 2014. "Consume Now or Later? Time Inconsistency, Collective Choice, and Revealed Preference," American Economic Review, American Economic Association, pages 4147-4183.
    2. Samuel Häfner, 2015. "Stable Biased Sampling," Working papers 2015/03, Faculty of Business and Economics - University of Basel.
    3. Ellison, Glenn & Fudenberg, Drew & Imhof, Lorens A., 2016. "Fast convergence in evolutionary models: A Lyapunov approach," Journal of Economic Theory, Elsevier, vol. 161(C), pages 1-36.
    4. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    5. H Peyton Young & Gabriel E. Kreindler, 2011. "Fast Convergence in Evolutionary Equilibrium Selection," Economics Series Working Papers 569, University of Oxford, Department of Economics.
    6. Azomahou, T. & Opolot, D., 2014. "Stability and strategic diffusion in networks," MERIT Working Papers 035, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    7. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society.
    8. Heller, Yuval & Mohlin, Erik, 2017. "When Is Social Learning Path-Dependent?," MPRA Paper 78962, University Library of Munich, Germany.
    9. Sandholm, William H., 2003. "Evolution and equilibrium under inexact information," Games and Economic Behavior, Elsevier, vol. 44(2), pages 343-378, August.
    10. Sandholm,W.H., 1999. "Markov evolution with inexact information," Working papers 15, Wisconsin Madison - Social Systems.
    11. repec:eee:jeborg:v:138:y:2017:i:c:p:63-68 is not listed on IDEAS
    12. García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.
    13. Kreindler, Gabriel E. & Young, H. Peyton, 2013. "Fast convergence in evolutionary equilibrium selection," Games and Economic Behavior, Elsevier, vol. 80(C), pages 39-67.
    14. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society.

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