# Coordination under global random interaction and local imitation

## Author

Listed:
• Abhimanyu Khan

()

## Abstract

Individuals are randomly matched to play a $$2\times 2$$ 2 × 2 coordination game where the Pareto efficient and risk dominant equilibria differ. Players choose strategies by imitating the strategy of the most successful individual they observe. So, while individuals interact globally, their observation and hence imitation, as determined by their social network, may be local. When all individuals observe each other, the most successful individual in the entire population is imitated; here, in the stochastically stable state, the population coordinates on the Pareto-efficient outcome. While this outcome is always stochastically stable, even when observability is incomplete, the state where everyone plays the action of the risk-dominant equilibrium may be stochastically stable as well. Reasonably tight sufficient conditions for unique stochastic stability of the state where all coordinate on the Pareto-efficient equilibrium strategy include each individual observing at least four other individuals or when each individual observes the same number of other individuals. These properties are readily generalisable to larger $$m\times m$$ m × m coordination games where the coordination outcomes can be Pareto-ranked. Copyright Springer-Verlag Berlin Heidelberg 2014

## Suggested Citation

• Abhimanyu Khan, 2014. "Coordination under global random interaction and local imitation," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 721-745, November.
• Handle: RePEc:spr:jogath:v:43:y:2014:i:4:p:721-745
DOI: 10.1007/s00182-013-0399-1
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File URL: http://hdl.handle.net/10.1007/s00182-013-0399-1

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## References listed on IDEAS

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1. Apesteguia, Jose & Huck, Steffen & Oechssler, Jorg, 2007. "Imitation--theory and experimental evidence," Journal of Economic Theory, Elsevier, vol. 136(1), pages 217-235, September.
2. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, vol. 70(1), pages 65-92, July.
3. Hedlund Jonas, 2012. "Altruism and Local Interaction," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-27, June.
4. Glenn Ellison & Drew Fudenberg, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 93-125.
5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
6. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 612-643, August.
7. Banerjee, Abhijit & Fudenberg, Drew, 2004. "Word-of-mouth learning," Games and Economic Behavior, Elsevier, vol. 46(1), pages 1-22, January.
8. 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.
9. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, Open Access Journal, vol. 1(4), pages 1-35, November.
10. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
11. Alos-Ferrer, Carlos & Weidenholzer, Simon, 2006. "Imitation, local interactions, and efficiency," Economics Letters, Elsevier, vol. 93(2), pages 163-168, November.
12. Friederike Mengel, 2009. "Conformism and cooperation in a local interaction model," Journal of Evolutionary Economics, Springer, vol. 19(3), pages 397-415, June.
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## Citations

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Cited by:

1. Fei Shi, 2015. "Long-run technology choice with endogenous local capacity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 377-399, June.
2. Abhimanyu Khan & Ronald Peeters & Frank Thuijsman & Philippe Uyttendaele, 2016. "Network Characteristics Enabling Efficient Coordination: A Simulation Study," Dynamic Games and Applications, Springer, vol. 6(4), pages 495-519, December.
3. Cui, Zhiwei & Wang, Rui, 2016. "Collaboration in networks with randomly chosen agents," Journal of Economic Behavior & Organization, Elsevier, vol. 129(C), pages 129-141.

### Keywords

Coordination games; Random matching; Local imitation; Stochastic stability; C73; D03;

### JEL classification:

• C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
• D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

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