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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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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384.
    2. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    3. Goyal, Sanjeev & Janssen, Maarten C. W., 1997. "Non-Exclusive Conventions and Social Coordination," Journal of Economic Theory, Elsevier, vol. 77(1), pages 34-57, November.
    4. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
    5. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    6. Anderlini, Luca & Ianni, Antonella, 1996. "Path Dependence and Learning from Neighbors," Games and Economic Behavior, Elsevier, vol. 13(2), pages 141-177, April.
    7. Weibull, Jörgen W. & van Damme, Eric, 1998. "Evolution with Mutations Driven by Control Costs," Working Paper Series 501, Research Institute of Industrial Economics.
    8. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-56, July.
    9. Bhaskar, V & Vega-Redondo, F, 1996. "Migration and the Evolution of Conventions," UFAE and IAE Working Papers 354.96, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    10. George J. Mailath & Larry Samuelson & Avner Shaked, 1997. "Endogenous Interactions," CARESS Working Papres endo-one, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
    11. repec:att:wimass:9324 is not listed on IDEAS
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    Cited by:
    1. Giorgio Fagiolo & Luigi Marengo & Marco Valente, 2003. "Endogenous Networks in Random Population Games," LEM Papers Series 2003/03, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    2. Fagiolo, Giorgio, 2005. "Endogenous neighborhood formation in a local coordination model with negative network externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 297-319, January.
    3. Matthew O. Jackson, 2003. "A survey of models of network formation: Stability and efficiency," Working Papers 1161, California Institute of Technology, Division of the Humanities and Social Sciences.
    4. Matthew O. Jackson & Alison Watts, 2000. "On the Formation of Interaction Networks in Social Coordination Games," Econometric Society World Congress 2000 Contributed Papers 0778, Econometric Society.
    5. Miguel A. Meléndez-Jiménez, 2007. "A Bargaining Approach To Coordination In Networks," Working Papers. Serie AD 2007-28, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    6. Michael Kosfeld, . "Network Experiments," IEW - Working Papers 152, Institute for Empirical Research in Economics - University of Zurich.
    7. 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, vol. 24(4), pages 383-408, June.
    8. Giorgio Fagiolo, 2002. "Coordination, Local Interactions, and Endogenous Neighborhood Formation," Computing in Economics and Finance 2002 98, Society for Computational Economics.
    9. Matthew O. Jackson, 2002. "The Stability and Efficiency of Economic and Social Networks," Microeconomics 0211011, EconWPA.
    10. Antoni Calvo-Armengol & Matthew O. Jackson, 2002. "Social Networks in Determining Employment and Wages: Patterns, Dynamics, and Inequality," Microeconomics 0211007, EconWPA.

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