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Optimal Equilibria of the Best Shot Game

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  • LUCA DALL’ASTA
  • PAOLO PIN
  • ABOLFAZL RAMEZANPOUR

Abstract

We consider any network environment in which the “best shot game” is played. This is the case where the possible actions are only two for every node (0 and 1), and the best response for a node is 1 if and only if all her neighbors play 0. A natural application of the model is one in which the action 1 is the purchase of a good, which is locally a public good, in the sense that it will be available also to neighbors. This game will typically exhibit a great multiplicity of equilibria. Imagine a social planner whose scope is to find an optimal equilibrium, i.e. one in which the number of nodes playing 1 is minimal. To find such an equilibrium is a very hard task for any non-trivial network architecture. We propose an implementable mechanism that, in the limit of infinite time, reaches an optimal equilibrium, even if this equilibrium and even the network structure is unknown to the social planner.

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Bibliographic Info

Article provided by Association for Public Economic Theory in its journal Journal of Public Economic Theory.

Volume (Year): 13 (2011)
Issue (Month): 6 (December)
Pages: 885-901

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Handle: RePEc:bla:jpbect:v:13:y:2011:i:6:p:885-901

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References

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  1. Andrea Galeotti & Sanjeev Goyal & Matthew O. Jackson & Fernando Vega-Redondo & Leeat Yariv, 2008. "Network Games," Economics Working Papers ECO2008/07, European University Institute.
    • Andrea Galeotti & Sanjeev Goyal & Matthew O. Jackson & Fernando Vega-Redondo & Leeat Yariv, 2010. "Network Games," Review of Economic Studies, Oxford University Press, vol. 77(1), pages 218-244.
  2. Matthew Haag & Roger Lagunoff, 1999. "Social Norms, Local Interaction, and Neighborhood Planning," Game Theory and Information 9907004, EconWPA.
  3. Dunia L�pez-Pintado, 2008. "The Spread of Free-Riding Behavior in a Social Network," Eastern Economic Journal, Palgrave Macmillan, vol. 34(4), pages 464-479.
  4. Jack Hirshleifer, 1983. "From weakest-link to best-shot: The voluntary provision of public goods," Public Choice, Springer, vol. 41(3), pages 371-386, January.
  5. Andrea Galeotti & Sanjeev Goyal, 2007. "The Law of the Few," Economics Discussion Papers 636, University of Essex, Department of Economics.
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Cited by:
  1. Subhasish M. Chowdhury & Dongryul Lee & Roman M. Sheremeta, 2011. "Top Guns May Not Fire: Best-Shot Group Contests with Group-Specific Public Good Prizes," University of East Anglia Applied and Financial Economics Working Paper Series 024, School of Economics, University of East Anglia, Norwich, UK..
  2. Boncinelli, Leonardo & Pin, Paolo, 2012. "Stochastic stability in best shot network games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 538-554.

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