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Network Formation with Endogenous Decay

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  • Francesco Feri

    (Ca’ Foscari University)

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    Abstract

    This paper considers a communication network characterized by an endogenous architecture and an imperfect transmission of information as in Bala and Goyal (2000). We propose a similar network's model with the difference that it is characterized by an endogenous rate of information decay. Endogenous decay is modelled as dependent on the result of a coordination game, played by every pair of directly linked agents and characterized by 2 equilibria: one efficient and the other risk dominant. Differently from other models, where the network represents only a channel to obtain information or to play a game, in our paper the network has an intrinsic value that depends on the chosen action in the coordination game by each participant. Moreover the endogenous network structure affects the play in the coordination game as well as the latter affects the network structure. The model has a multiplicity of equilibria and we produce a full characterization of those are stochastically stable. For sufficiently low link costs we find that in stochastically stable states network structure is ever efficient; individuals can be coordinated on efficient as well as on risk dominant action depending on the decay difference among the two equilibria in the single coordination game. For high link costs stochastically stable states can display networks that are not efficient; individuals are never coordinated on the efficient action.

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    Bibliographic Info

    Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2005.35.

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    Date of creation: Mar 2005
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    Handle: RePEc:fem:femwpa:2005.35

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    Keywords: Network; Decay; Strategical interaction;

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    1. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
    2. 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.
    3. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
    4. Arthur J Robson & Fernando Vega-Redondo, 1999. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Levine's Working Paper Archive 2112, David K. Levine.
    5. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
    6. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
    7. Sanjeev Goyal & Fernando Vega-Redondo, 2000. "Learning, Network Formation and Coordination," Tinbergen Institute Discussion Papers 00-093/1, Tinbergen Institute.
    8. Jackson, Matthew O. & Watts, Alison, 2002. "On the formation of interaction networks in social coordination games," Games and Economic Behavior, Elsevier, vol. 41(2), pages 265-291, November.
    9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    10. Selten,Reinhard, . "Evolution,learning and economic behaviour," Discussion Paper Serie B 132, University of Bonn, Germany.
    11. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
    12. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
    13. Karandikar, Rajeeva & Mookherjee, Dilip & Ray, Debraj & Vega-Redondo, Fernando, 1998. "Evolving Aspirations and Cooperation," Journal of Economic Theory, Elsevier, vol. 80(2), pages 292-331, June.
    14. H. Peyton Young, 1996. "The Economics of Convention," Journal of Economic Perspectives, American Economic Association, vol. 10(2), pages 105-122, Spring.
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