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Optimal Equilibria of the Best Shot Game

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  • Paolo Pin

    (Università degli Studi di Siena)

  • Luca Dall'Asta
  • Abolfazl Ramezanpour

    (Politecnico di Torino
    he Abdus Salam International Centre for Theoretical Physics)

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

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2009.33.

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Date of creation: May 2009
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Handle: RePEc:fem:femwpa:2009.33

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Keywords: Networks; Best Shot Game; Simulated Annealing;

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  1. Matthew Haag & Roger Lagunoff, 2006. "Social Norms, Local Interaction, And Neighborhood Planning ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(1), pages 265-296, 02.
  2. 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).
  3. 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.
  4. Andrea Galeotti & Sanjeev Goyal, 2007. "The Law of the Few," Economics Discussion Papers 636, University of Essex, Department of Economics.
  5. 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.
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Cited by:
  1. Boncinelli, Leonardo & Pin, Paolo, 2012. "Stochastic stability in best shot network games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 538-554.
  2. 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..

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