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

## Author

Listed:
• 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

## Suggested Citation

• Boyu Zhang & Josef Hofbauer, 2015. "Equilibrium selection via replicator dynamics in $$2 \times 2$$ 2 × 2 coordination games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 433-448, May.
• Handle: RePEc:spr:jogath:v:44:y:2015:i:2:p:433-448
DOI: 10.1007/s00182-014-0437-7
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## References listed on IDEAS

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## Citations

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Cited by:

1. Zhang, Boyu & Hofbauer, Josef, 2016. "Quantal response methods for equilibrium selection in 2×2 coordination games," Games and Economic Behavior, Elsevier, vol. 97(C), pages 19-31.
2. Zhang, Boyu, 2016. "Quantal response methods for equilibrium selection in normal form games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 113-123.
3. Benndorf, Volker & Martínez-Martínez, Ismael & Normann, Hans-Theo, 2021. "Games with coupled populations: An experiment in continuous time," Journal of Economic Theory, Elsevier, vol. 195(C).
4. Rongwu Lu & Xinhua Wang & Hao Yu & Dan Li, 2018. "Multiparty Evolutionary Game Model in Coal Mine Safety Management and Its Application," Complexity, Hindawi, vol. 2018, pages 1-10, March.
5. Sofia B. S. D. Castro, 2018. "Learning by replicator and best-response: the importance of being indifferent," Journal of Evolutionary Economics, Springer, vol. 28(4), pages 985-999, September.

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## More about this item

### Keywords

Equilibrium selection; Replicator dynamics; Risk dominance; Basins of attraction; C62; C73; D58;
All these keywords.

### JEL classification:

• C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
• C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
• D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models

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