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 \(2 \times 2\) 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.
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Acknowledgments
We are grateful to Mathias Staudigl and Christian Hilbe for helpful discussions. We also thank the associate editor and two anonymous reviewers for useful comments. This research received financial support from the NSFC (Project No. 11301032) of China, “the Fundamental Research Funds for the Central Universities” of China and the Viennese WWTF (Project No. MA09-017) of Austria.
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Zhang, B., Hofbauer, J. Equilibrium selection via replicator dynamics in \(2 \times 2\) coordination games. Int J Game Theory 44, 433–448 (2015). https://doi.org/10.1007/s00182-014-0437-7
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DOI: https://doi.org/10.1007/s00182-014-0437-7