# Equilibrium selection via replicator dynamics in $$2 \times 2$$ 2 × 2 coordination games

## Author Info

Listed author(s):
• Boyu Zhang

()

• Josef Hofbauer

()

## Abstract

This paper studies two equilibrium selection methods based on replicator dynamics. A Nash equilibrium is called centroid dominant if the trajectory of the replicator dynamics starting at the centroid of the strategy simplex converges to it. On the other hand, an equilibrium is called basin dominant if it has the largest basin of attraction. These two concepts are compared with risk dominance in the context of $$2 \times 2$$ 2 × 2 bimatrix coordination games. The main results include (a) if a Nash equilibrium is both risk dominant and centroid dominant, it must have the largest basin of attraction, (b) the basin dominant equilibrium must be risk dominant or centroid dominant. Copyright Springer-Verlag Berlin Heidelberg 2015

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File URL: http://hdl.handle.net/10.1007/s00182-014-0437-7

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## Bibliographic Info

Article provided by Springer & Game Theory Society in its journal International Journal of Game Theory.

Volume (Year): 44 (2015)
Issue (Month): 2 (May)
Pages: 433-448

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 Handle: RePEc:spr:jogath:v:44:y:2015:i:2:p:433-448 DOI: 10.1007/s00182-014-0437-7 Contact details of provider: Web page: http://www.springer.com Order Information: Web: http://www.springer.com/economics/economic+theory/journal/182/PS2

## References

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1. Hofbauer, Josef & Sorger, Gerhard, 1999. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Journal of Economic Theory, Elsevier, vol. 85(1), pages 1-23, March.
2. Russell Golman & Scott Page, 2010. "Basins of attraction and equilibrium selection under different learning rules," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 73-75, January.
3. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
4. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
5. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
6. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
7. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
8. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
10. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
11. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
12. Russell Golman & Scott Page, 2010. "Basins of attraction and equilibrium selection under different learning rules," Journal of Evolutionary Economics, Springer, vol. 20(1), pages 49-72, January.
13. Kim, Youngse, 1996. "Equilibrium Selection inn-Person Coordination Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 203-227, August.
14. J. Hofbauer, 1999. "The spatially dominant equilibrium of a game," Annals of Operations Research, Springer, vol. 89(0), pages 233-251, January.
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