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Replicator Dynamics and Evolutionary Stable Strategies in Heterogeneous Games

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

Abstract

We generalise and extend the work of Inarra and Laruelle (2011) by studying two person symmetric evolutionary games with two strategies, a heterogeneous population with two possible types of individuals and incomplete information. Comparing such games with their classic homogeneous version with 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.

Suggested Citation

  • André Barreira da Silva Rocha & Annick Laruelle & Peio Zuazo, 2012. "Replicator Dynamics and Evolutionary Stable Strategies in Heterogeneous Games," Discussion Papers in Economics 11/54, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:11/54
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    References listed on IDEAS

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    1. Daniel Friedman, 1998. "On economic applications of evolutionary game theory," Journal of Evolutionary Economics, Springer, vol. 8(1), pages 15-43.
    2. 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.
    3. 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.
    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. 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.
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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 http://www-fae1-eao1-ehu-, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    2. 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.
    3. Rosas-Martinez, Victor H., 2016. "Expectations Over Durable Assets: How to Avoid the Formation of Value Bubbles," MPRA Paper 75350, University Library of Munich, Germany.
    4. 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.
    5. Victor H. ROSAS-MARTINEZ, 2016. "On Behavioral Macroeconomics, Globalization, and Economic Growth," Journal of Economics Bibliography, KSP Journals, vol. 3(3), pages 482-489, September.

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