# Almost global convergence to p-dominant equilibrium

## Author

Listed:
• William H. Sandholm

() (Department of Economics, University of Wisconsin, 1180 Observatory Drive, Madison, WI 53706)

## 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.

## Suggested Citation

• William H. Sandholm, 2001. "Almost global convergence to p-dominant equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 107-116.
• Handle: RePEc:spr:jogath:v:30:y:2001:i:1:p:107-116
Note: Received December 1999/Revised version November 2000
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## References listed on IDEAS

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1. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
2. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
3. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-157, January.
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. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
6. 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.
7. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
Full references (including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:

1. Kreindler, Gabriel E. & Young, H. Peyton, 2013. "Fast convergence in evolutionary equilibrium selection," Games and Economic Behavior, Elsevier, vol. 80(C), pages 39-67.
2. repec:eee:gamebe:v:107:y:2018:i:c:p:109-122 is not listed on IDEAS
3. 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).
4. Sandholm,W.H., 1999. "Markov evolution with inexact information," Working papers 15, Wisconsin Madison - Social Systems.
5. H Peyton Young & Gabriel E. Kreindler, 2012. "Rapid Innovation Diffusion in Social Networks," Economics Series Working Papers 626, University of Oxford, Department of Economics.
6. Heller, Yuval & Mohlin, Erik, 2017. "When Is Social Learning Path-Dependent?," MPRA Paper 78962, University Library of Munich, Germany.
7. He, Simin & Wu, Jiabin, 2018. "Compromise and Coordination: An Experimental Study," MPRA Paper 84713, University Library of Munich, Germany.
8. Häfner, Samuel, 2018. "Stable biased sampling," Games and Economic Behavior, Elsevier, vol. 107(C), pages 109-122.
9. 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.
10. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
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. Oyama, Daisuke & Sandholm, William H. & Tercieux, Olivier, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
14. Sandholm, William H., 2003. "Evolution and equilibrium under inexact information," Games and Economic Behavior, Elsevier, vol. 44(2), pages 343-378, August.

### Keywords

evolutionary game theory; coordination games;

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