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Evolution of Conventions in Endogenous Social Networks

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  • Edward Droste

    (Tilburg University)

  • Robert P. Gilles

    (Virginia Polytechnic Institute)

  • Cathleen Johnson

    (Virginia Polytechnic Institute)

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    Abstract

    We analyze the dynamic implications of learning in a large population coordination game where both the actions of the players and the communication network between these players evolve over time. We depart from the conventional models in assuming that the interaction network itself is subject to evolutionary pressure. Cost considerations of social interaction are incorporated by application of a circular model in which all players are located at equal distances along a circle. Although the locations of the players are fixed they can create their own interaction neighborhood by forming and severing links with other players. The spatial structure of the model is then used to determine the costs of establishing a communication link between a pair of players. Namely, we assume that the larger the distance between two players on the circle, the larger the maintenance costs of the mutual link will be. As maintenance costs include invested time and effort, distance should not only be interpreted as physical distance but may also represent social distance. We follow standard evolutionary game theoretic practice to determine the equilibria in this setting. The resulting equilibrium represents the players' medium run behavior if perturbations representing players' mistakes are absent. We find that in this medium run case, the dynamic process converges to an absorbing state. These absorbing states include ones in which there emerge local conventions, i.e., fully connected neighborhoods of players who coordinate on the same strategy. In the ultralong run, i.e., when perturbations representing players' mistakes are taken into account, coexistence of conventions is no longer possible. We show that the risk-dominant convention is the unique stochastically stable convention, meaning that it will be observed almost surely when the mistake probabilities are small but nonvanishing. This confirms the insights obtained in Ellison (1993) for fixed spatial interaction structures.

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    Bibliographic Info

    Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0594.

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    Date of creation: 01 Aug 2000
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    Handle: RePEc:ecm:wc2000:0594

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    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
    2. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, Elsevier, vol. 71(1), pages 44-74, October.
    3. Bhaskar, V. & Vega-Redondo, Fernando, 2004. "Migration and the evolution of conventions," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 55(3), pages 397-418, November.
    4. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
    5. J. Bergin & B. Lipman, 2010. "Evolution with State-Dependent Mutations," Levine's Working Paper Archive 486, David K. Levine.
    6. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262582384, December.
    7. George J. Mailath & Larry Samuelson & Avner Shaked, 1997. "Endogenous Interactions," CARESS Working Papres, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences endo-one, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
    8. Goyal, Sanjeev & Janssen, Maarten C. W., 1997. "Non-Exclusive Conventions and Social Coordination," Journal of Economic Theory, Elsevier, Elsevier, vol. 77(1), pages 34-57, November.
    9. repec:att:wimass:9324 is not listed on IDEAS
    10. Eric Van Damme & Jorgen W Weibull, 1999. "Evolution with Mutations Driven by Control Costs," Levine's Working Paper Archive 2113, David K. Levine.
    11. Anderlini, Luca & Ianni, Antonella, 1996. "Path Dependence and Learning from Neighbors," Games and Economic Behavior, Elsevier, Elsevier, vol. 13(2), pages 141-177, April.
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    Cited by:
    1. Jackson, Matthew O. & Calvo, Antoni, 2002. "Social Networks in Determing Employment and Wages: Patterns, Dynamics, and Inequality," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1149, California Institute of Technology, Division of the Humanities and Social Sciences.
    2. Giorgio Fagiolo, 2002. "Coordination, Local Interactions, and Endogenous Neighborhood Formation," Computing in Economics and Finance 2002, Society for Computational Economics 98, Society for Computational Economics.
    3. Jackson, Matthew O. & Watts, Alison, 2002. "On the formation of interaction networks in social coordination games," Games and Economic Behavior, Elsevier, Elsevier, vol. 41(2), pages 265-291, November.
    4. Giorgio Fagiolo & Luigi Marengo & Marco Valente, . "Endogenous Networks in Random Population Games," Modeling, Computing, and Mastering Complexity 2003, Society for Computational Economics 05, Society for Computational Economics.
    5. Matthew O. Jackson, 2003. "A Survey of Models of Network Formation: Stability and Efficiency," Game Theory and Information, EconWPA 0303011, EconWPA.
    6. Fagiolo, Giorgio, 2005. "Endogenous neighborhood formation in a local coordination model with negative network externalities," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 29(1-2), pages 297-319, January.
    7. Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics, EconWPA 0211011, EconWPA.
    8. Miguel A. Meléndez-Jiménez, 2007. "A Bargaining Approach To Coordination In Networks," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2007-28, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. Michael Kosfeld, . "Network Experiments," IEW - Working Papers 152, Institute for Empirical Research in Economics - University of Zurich.
    10. Giorgio Fagiolo & Luigi Marengo & Marco Valente, 2005. "Population Learning in a Model with Random Payoff Landscapes and Endogenous Networks," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 24(4), pages 383-408, June.
    11. A. Arrighetti & S. Curatolo, 2010. "Costi di coordinamento e vantaggi di aggregazione: esiti, morfologia e processi di interazione in un mondo artificiale multi-agente," Economics Department Working Papers 2010-EP01, Department of Economics, Parma University (Italy).

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