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Optimal Equilibria of the Best Shot Game


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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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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  1. Matthew Haag & Roger Lagunoff, 2000. "social Norms, Local Interaction and Neighborhood Planning," Levine's Working Paper Archive 2049, David K. Levine.
  2. 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.
  3. Dunia Lopez Pintado, 2007. "The Spread of Free-Riding Behavior in a Social Network," UFAE and IAE Working Papers 718.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. Andrea Galeotti & Sanjeev Goyal, 2010. "The Law of the Few," American Economic Review, American Economic Association, vol. 100(4), pages 1468-92, September.
  5. 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.
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