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Optimal Equilibria of the Best Shot Game

Author

Listed:
  • 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.

Suggested Citation

  • Paolo Pin & Luca Dall'Asta & Abolfazl Ramezanpour, 2009. "Optimal Equilibria of the Best Shot Game," Working Papers 2009.33, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2009.33
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    References listed on IDEAS

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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, February.
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    4. Andrea Galeotti & Sanjeev Goyal, 2010. "The Law of the Few," American Economic Review, American Economic Association, vol. 100(4), pages 1468-1492, 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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    Cited by:

    1. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Chowdhury, Subhasish M. & Lee, Dongryul & Sheremeta, Roman M., 2013. "Top guns may not fire: Best-shot group contests with group-specific public good prizes," Journal of Economic Behavior & Organization, Elsevier, vol. 92(C), pages 94-103.
    3. Jean Philippe Bouchaud & Matteo Marsili & Jean-Pierre Nadal, 2023. "Application of spin glass ideas in social sciences, economics and finance," Post-Print hal-04145594, HAL.
    4. Fabrizio Altarelli & Alfredo Braunstein & Luca Dall’Asta, 2015. "Statics and Dynamics of Selfish Interactions in Distributed Service Systems," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-29, July.
    5. Jin, Xing & Tao, Yuchen & Wang, Jingrui & Wang, Chao & Wang, Yongheng & Zhang, Zhouyang & Wang, Zhen, 2023. "Strategic use of payoff information in k-hop evolutionary Best-shot networked public goods game," Applied Mathematics and Computation, Elsevier, vol. 459(C).
    6. Papadimitriou, Christos & Peng, Binghui, 2023. "Public goods games in directed networks," Games and Economic Behavior, Elsevier, vol. 139(C), pages 161-179.
    7. Boncinelli, Leonardo & Pin, Paolo, 2012. "Stochastic stability in best shot network games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 538-554.
    8. Jean-Philippe Bouchaud & Matteo Marsili & Jean-Pierre Nadal, 2023. "Application of spin glass ideas in social sciences, economics and finance," Papers 2306.16165, arXiv.org.

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    More about this item

    Keywords

    Networks; Best Shot Game; Simulated Annealing;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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