# Sophisticated imitation in cyclic games

## Author Info

• Josef Hofbauer

()
(Department of Mathematics, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria)

• Karl H. Schlag

()
(Economics Department, European University Institute, Via dei Roccettini 9, 50016 San Domenico di Fiesole, Italy)

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## Abstract

Individuals belonging to two large populations are repeatedly randomly matched to play a cyclic $2\times 2$ game such as Matching Pennies. Between matching rounds, individuals sometimes change their strategy after observing a finite sample of other outcomes within their population. Individuals from the same population follow the same behavioral rule. In the resulting discrete time dynamics the unique Nash equilibrium is unstable. However, for sample sizes greater than one, we present an imitation rule where long run play cycles closely around the equilibrium.

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## Bibliographic Info

Article provided by Springer in its journal Journal of Evolutionary Economics.

Volume (Year): 10 (2000)
Issue (Month): 5 ()
Pages: 523-543

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Handle: RePEc:spr:joevec:v:10:y:2000:i:5:p:523-543

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## Related research

Keywords: Strictly improving - Matching pennies game - Replicator dynamics - Limit cycle - Discretization;

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Find related papers by JEL classification:
• C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

## References

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## Citations

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Cited by:
1. Theo Offerman & Andrew Schotter, 2007. "Imitation and Luck: An Experimental Study on Social Sampling," Working Papers 0020, New York University, Center for Experimental Social Science.
2. Lipatov, Vilen, 2003. "Evolution of Tax Evasion," MPRA Paper 966, University Library of Munich, Germany, revised 06 Dec 2005.
3. Güth, Werner & Kliemt, Hartmut & Peleg, Bezalel, 1998. "Co-evolution of preferences and information in simple games of trust," SFB 373 Discussion Papers 1998,72, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
4. Alanyali, Murat, 2010. "A note on adjusted replicator dynamics in iterated games," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 86-98, January.
5. Ana B. Ania, 2000. "Learning by Imitation when Playing the Field," Vienna Economics Papers 0005, University of Vienna, Department of Economics.
6. Abhijit Banerjee & Drew Fudenberg, 2010. "Word of Mouth Learning," Levine's Working Paper Archive 723, David K. Levine.
7. Alan Beggs, 2002. "On the Convergence of Reinforcement Learning," Economics Series Working Papers 96, University of Oxford, Department of Economics.
8. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.

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