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Replicator Dynamics and Evolutionary Stable Strategies in Heterogeneous Games

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  • Zuazo Garín, Peio
  • Rocha, André Barreira da Silva
  • Laruelle, Annick

Abstract

We generalise and extend the work of Iñarra and Laruelle (2011) by studying two person symmetric evolutionary games with two strategies, a heterogenous population with two possible types of individuals and incomplete information. Comparing such games with their classic homogeneous version vith complete information found in the literature, we show that for the class of anti-coordination games the only evolutionarily stable strategy vanishes. Instead, we find infinite neutrally stable strategies. We also model the evolutionary process using two different replicator dynamics setups, each with a different inheritance rule, and we show that both lead to the same results with respect to stability.

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Paper provided by Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I in its series IKERLANAK with number 2011-57.

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Date of creation: Dec 2011
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Handle: RePEc:ehu:ikerla:6608

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Postal: Dpto. de Fundamentos del Análisis Económico I, Facultad de CC. Económicas y Empresariales, Universidad del País Vasco, Avda. Lehendakari Aguirre 83, 48015 Bilbao, Spain
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  1. Xu, C. & Ji, M. & Yap, Yee Jiun & Zheng, Da-Fang & Hui, P.M., 2011. "Costly punishment and cooperation in the evolutionary snowdrift game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1607-1614.
  2. Daniel Friedman, 1998. "On economic applications of evolutionary game theory," Journal of Evolutionary Economics, Springer, vol. 8(1), pages 15-43.
  3. Platkowski, Tadeusz & Zakrzewski, Jan, 2011. "Asymptotically stable equilibrium and limit cycles in the Rock–Paper–Scissors game in a population of players with complex personalities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4219-4226.
  4. Ross Cressman & Jean-Francois Wen & William Morrison, 1998. "On the Evolutionary Dynamics of Crime," Canadian Journal of Economics, Canadian Economics Association, vol. 31(5), pages 1101-1117, November.
  5. Iñarra García, María Elena & Laruelle, Annick, 2011. "Discriminating by Tagging: Artificial Distinction, Real Discrimination," IKERLANAK 2011-50, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
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Cited by:
  1. Barreira da Silva Rocha, André & Laruelle, Annick, 2012. "Evolution of Cooperation in the Snowdrift Game with Incomplete Information and Heterogeneous Population," IKERLANAK 2012-62, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  2. Barreira da Silva Rocha, André, 2013. "Evolutionary dynamics of nationalism and migration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3183-3197.

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