International Journal of Game Theory

, Volume 44, Issue 2, pp 433–448 | Cite as

Equilibrium selection via replicator dynamics in \(2 \times 2\) coordination games

Article
First Online:
Accepted:

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.

Keywords

Equilibrium selection Replicator dynamics Risk dominance  Basins of attraction 

JEL Classification

C62 C73 D58 
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Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Laboratory of Mathematics and Complex Systems, Ministry of EducationSchool of Mathematical Sciences, Beijing Normal UniversityBeijingPeople’s Republic of China
  2. 2.Faculty of MathematicsUniversity of ViennaViennaAustria

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