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Evolution of Conventions in Endogenous Social Networks

  • Edward Droste

    (Tilburg University)

  • Robert P. Gilles

    (Virginia Polytechnic Institute)

  • Cathleen Johnson

    (Virginia Polytechnic Institute)

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    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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    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. BERGIN, James & LIPMAN, Bart, 1994. "Evolution with State-Dependent Mutations," CORE Discussion Papers 1994055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. repec:att:wimass:9324 is not listed on IDEAS
    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. Aderlini, L. & Ianni, A., 1993. "Path Dependence and Learning from Neighbours," Papers 186, Cambridge - Risk, Information & Quantity Signals.
    6. Eric Van Damme & Jorgen W Weibull, 1999. "Evolution with Mutations Driven by Control Costs," Levine's Working Paper Archive 2113, David K. Levine.
    7. 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, June.
    8. 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.
    9. Matthew O. Jackson & Asher Wolinsky, 1995. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Fernando Vega Redondo & Ventakamaran Bhaskar, 1996. "Migration and the evolution of conventions," Working Papers. Serie AD 1996-23, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    11. 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.
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