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Almost global convergence to p-dominant equilibrium

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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, vol. 63(1), pages 145-157, January.
    2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    3. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    4. Saez-Marti, Maria & Weibull, Jorgen W., 1999. "Clever Agents in Young's Evolutionary Bargaining Model," Journal of Economic Theory, Elsevier, vol. 86(2), pages 268-279, June.
    5. 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.
    6. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
    7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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    Citations

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    Cited by:

    1. H Peyton Young & Gabriel E. Kreindler, 2012. "Rapid Innovation Diffusion in Social Networks," Economics Series Working Papers 626, University of Oxford, Department of Economics.
    2. Häfner, Samuel, 2018. "Stable biased sampling," Games and Economic Behavior, Elsevier, vol. 107(C), pages 109-122.
    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. Kreindler, Gabriel E. & Young, H. Peyton, 2013. "Fast convergence in evolutionary equilibrium selection," Games and Economic Behavior, Elsevier, vol. 80(C), pages 39-67.
    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. Oyama, Daisuke & Sandholm, William H. & Tercieux, Olivier, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    8. He, Simin & Wu, Jiabin, 2018. "Compromise and Coordination: An Experimental Study," MPRA Paper 84713, University Library of Munich, Germany.
    9. Heller, Yuval & Mohlin, Erik, 2017. "When Is Social Learning Path-Dependent?," MPRA Paper 78962, University Library of Munich, Germany.
    10. Sandholm, William H., 2003. "Evolution and equilibrium under inexact information," Games and Economic Behavior, Elsevier, vol. 44(2), pages 343-378, August.
    11. Sandholm,W.H., 1999. "Markov evolution with inexact information," Working papers 15, Wisconsin Madison - Social Systems.
    12. repec:eee:jeborg:v:138:y:2017:i:c:p:63-68 is not listed on IDEAS
    13. 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.

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