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Cooperation through Imitation and Exclusion in Networks

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  • Mengel, Friederike
  • Fosco, Constanza

Abstract

We develop a simple model to study the coevolution of interaction structures and action choices in prisoners' dilemma games. Agents are boundedly rational and choose both actions and interaction partners via payoff-biased imitation. The dynamics of imitation and exclusion yields polymorphic outcomes under a wide range of parameters. Whenever agents hold some information beyond their interaction neighbors defectors and cooperators always coexist in disconnected components. Otherwise polymorphic networks can emerge with a center of cooperators and a periphery of defectors. Any stochastically stable state has at most two disconnected components. Simulations confirm our analytical results and show that the share of cooperators increases with the speed at which the network evolves, increases with the radius of interaction and decreases with the radius of information.

Suggested Citation

  • Mengel, Friederike & Fosco, Constanza, 2007. "Cooperation through Imitation and Exclusion in Networks," MPRA Paper 5258, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:5258
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    Cited by:

    1. García-Martínez, José A. & Vega-Redondo, Fernando, 2015. "Social cohesion and the evolution of altruism," Games and Economic Behavior, Elsevier, vol. 92(C), pages 74-105.
    2. Brañas-Garza, Pablo & Cobo-Reyes, Ramón & Espinosa, María Paz & Jiménez, Natalia & Kovárík, Jaromír & Ponti, Giovanni, 2010. "Altruism and social integration," Games and Economic Behavior, Elsevier, vol. 69(2), pages 249-257, July.
      • Brañas Garza, Pablo & Cobo Reyes, Ramón & Espinosa Alejos, María Paz & Jiménez, Natalia & Kovarik, Jaromir & Ponti, Giovanni, 2009. "Altruism and Social Integration," IKERLANAK 2009-35, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
      • Brañas Garza, Pablo & Cobo Reyes, Ramón & Espinosa Alejos, María Paz & Jiménez, Natalia & Kovarik, Jaromir & Ponti, Giovanni, 2009. "Altruism and Social Integration," DFAEII Working Papers 2009-35, University of the Basque Country - Department of Foundations of Economic Analysis II.
    3. Zhiwei Cui, 2019. "Matching, Imitation, and Coordination in Networks," Dynamic Games and Applications, Springer, vol. 9(1), pages 47-67, March.
    4. Kovarik, Jaromir & Jiménez, Natalia & Ponti, Giovanni & Espinosa Alejos, María Paz & Brañas Garza, Pablo & Cobo Reyes, Ramón, 2009. "Altruism and Social Integration," IKERLANAK 2009-35, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    5. Tsakas, Nikolas, 2017. "Diffusion by imitation: The importance of targeting agents," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 118-151.
    6. Chih‐Sheng Hsieh & Lung‐Fei Lee & Vincent Boucher, 2020. "Specification and estimation of network formation and network interaction models with the exponential probability distribution," Quantitative Economics, Econometric Society, vol. 11(4), pages 1349-1390, November.
    7. Tsakas, Nikolas, 2012. "Naive learning in social networks: Imitating the most successful neighbor," MPRA Paper 37796, University Library of Munich, Germany.
    8. Ludo Waltman & Nees Eck & Rommert Dekker & Uzay Kaymak, 2013. "An Evolutionary Model of Price Competition Among Spatially Distributed Firms," Computational Economics, Springer;Society for Computational Economics, vol. 42(4), pages 373-391, December.
    9. Ladley, Daniel & Wilkinson, Ian & Young, Louise, 2015. "The impact of individual versus group rewards on work group performance and cooperation: A computational social science approach," Journal of Business Research, Elsevier, vol. 68(11), pages 2412-2425.
    10. Pin, Paolo & Rogers, Brian W., 2015. "Cooperation, punishment and immigration," Journal of Economic Theory, Elsevier, vol. 160(C), pages 72-101.
    11. Hedlund Jonas, 2012. "Altruism and Local Interaction," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-27, June.
    12. Friederike Mengel, 2009. "Conformism and cooperation in a local interaction model," Journal of Evolutionary Economics, Springer, vol. 19(3), pages 397-415, June.
    13. Wilhite, Allen, 2014. "Network structure, games, and agent dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 225-238.
    14. Sebastian J. Goerg & David B. Johnson & Jonathan D. Rogers, 2017. "Endowments, Perceived Similarity, And Dictator Giving," Economic Inquiry, Western Economic Association International, vol. 55(2), pages 1130-1144, April.
    15. Brañas-Garza, Pablo & Cobo-Reyes, Ramón & Espinosa, María Paz & Jiménez, Natalia & Kovárík, Jaromír & Ponti, Giovanni, 2010. "Altruism and social integration," Games and Economic Behavior, Elsevier, vol. 69(2), pages 249-257, July.
    16. Jaromír Kovářík & Friederike Mengel & José Gabriel Romero, 2018. "Learning in network games," Quantitative Economics, Econometric Society, vol. 9(1), pages 85-139, March.
      • Kovarik, Jaromir & Mengel, Friederike & Romero, José Gabriel, 2012. "Learning in Network Games," IKERLANAK Ikerlanak;2012-66, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    17. Cui, Zhiwei, 2014. "More neighbors, more efficiency," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 103-115.
    18. Zeng, Weijun & Ai, Hongfeng & Zhao, Man, 2019. "Asymmetrical expectations of future interaction and cooperation in the iterated prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 148-164.
    19. Hong, Lijun & Geng, Yini & Du, Chunpeng & Shen, Chen & Shi, Lei, 2021. "Average payoff-driven or imitation? A new evidence from evolutionary game theory in finite populations," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    20. Antinyan, Armenak & Horváth, Gergely & Jia, Mofei, 2019. "Social status competition and the impact of income inequality in evolving social networks: An agent-based model," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 79(C), pages 53-69.
    21. Edward J. Cartwright, 2014. "Imitation And Coordination In Small‐World Networks," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 21(2), pages 71-90, April.
    22. Wilson, James & Hill, J. & Kersula, M. & Wilson, C.L. & Whitsel, L. & Yan, L. & Acheson, J. & Chen, Y. & Cleaver, C. & Congdon, C. & Hayden, A. & Hayes, P. & Johnson, T. & Morehead, G. & Steneck, R. &, 2013. "Costly information and the evolution of self-organization in a small, complex economy," Journal of Economic Behavior & Organization, Elsevier, vol. 90(S), pages 76-93.
    23. Herings, P. Jean-Jacques & Peeters, Ronald & Tenev, Anastas & Thuijsman, Frank, 2019. "Naïve imitation and partial cooperation in a local public goods model," Research Memorandum 013, Maastricht University, Graduate School of Business and Economics (GSBE).
    24. Daniel Ladley & Ian Wilkinson & Louise Young, 2013. "The Evolution Of Cooperation In Business: Individual Vs. Group Incentives," Discussion Papers in Economics 13/14, Division of Economics, School of Business, University of Leicester.

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    Keywords

    Game Theory; Cooperation; Imitation Learning; Network Formation;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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