IDEAS home Printed from https://ideas.repec.org/p/fem/femwpa/2009.33.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://feem-media.s3.eu-central-1.amazonaws.com/wp-content/uploads/NDL2009-033.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    2. Andrea Galeotti & Sanjeev Goyal & Matthew O. Jackson & Fernando Vega-Redondo & Leeat Yariv, 2010. "Network Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 218-244.
    3. Dunia López-Pintado, 2008. "The Spread of Free-Riding Behavior in a Social Network," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 34(4), pages 464-479.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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," Papers 2306.16165, arXiv.org.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Boncinelli, Leonardo & Pin, Paolo, 2012. "Stochastic stability in best shot network games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 538-554.
    3. Arthur Schram & Boris Van Leeuwen & Theo Offerman, 2013. "Superstars Need Social Benefits: An Experiment on Network Formation," Working Papers 1306, Departament Empresa, Universitat Autònoma de Barcelona, revised Jul 2013.
    4. Allouch, Nizar, 2017. "The cost of segregation in (social) networks," Games and Economic Behavior, Elsevier, vol. 106(C), pages 329-342.
    5. Myeonghwan Cho, 2010. "Endogenous formation of networks for local public goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 529-562, October.
    6. Zhang, Yang & Du, Xiaomin, 2017. "Network effects on strategic interactions: A laboratory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 143(C), pages 133-146.
    7. Boris van Leeuwen & Theo Offerman & Arthur Schram, 2020. "Competition for Status Creates Superstars: an Experiment on Public Good Provision and Network Formation," Journal of the European Economic Association, European Economic Association, vol. 18(2), pages 666-707.
    8. Andrea Galeotti & Luca Paolo Merlino, 2014. "Endogenous Job Contact Networks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(4), pages 1201-1226, November.
    9. Allouch, Nizar, 2015. "On the private provision of public goods on networks," Journal of Economic Theory, Elsevier, vol. 157(C), pages 527-552.
    10. 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.
    11. , D. & Tessone, Claudio J. & ,, 2014. "Nestedness in networks: A theoretical model and some applications," Theoretical Economics, Econometric Society, vol. 9(3), September.
    12. , David, 2016. "The formation of networks with local spillovers and limited observability," Theoretical Economics, Econometric Society, vol. 11(3), September.
    13. Acemoglu, Daron & Makhdoumi, Ali & Malekian, Azarakhsh & Ozdaglar, Asuman, 2017. "Privacy-constrained network formation," Games and Economic Behavior, Elsevier, vol. 105(C), pages 255-275.
    14. M. Koenig & Claudio J. Tessone & Yves Zenou, "undated". "A Dynamic Model of Network Formation with Strategic Interactions," Working Papers CCSS-09-006, ETH Zurich, Chair of Systems Design.
    15. Subhasish M. Chowdhury & Iryna Topolyan, 2013. "The Attack-and-Defence Group Contests," University of East Anglia Applied and Financial Economics Working Paper Series 049, School of Economics, University of East Anglia, Norwich, UK..
    16. Camacho, Carmen & Hassan, Waleed, 2023. "The dynamics of revolution: Discrimination, social unrest and the optimal timing of revolution," Economic Modelling, Elsevier, vol. 128(C).
    17. Sergio Currarini & Carmen Marchiori & Alessandro Tavoni, 2016. "Network Economics and the Environment: Insights and Perspectives," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(1), pages 159-189, September.
    18. Daniel E. O'Leary, 2018. "DNA Mining and genealogical information systems: Not just for finding family ethnicity," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 25(4), pages 190-196, October.
    19. Eunae Yoo & Elliot Rabinovich & Bin Gu, 2020. "The Growth of Follower Networks on Social Media Platforms for Humanitarian Operations," Production and Operations Management, Production and Operations Management Society, vol. 29(12), pages 2696-2715, December.
    20. Atallah, Shadi S. & Huang, Ju-Chin & Leahy, Jessica & Bennett, Karen, 2020. "Preference Heterogeneity and Neighborhood Effect in Invasive Species Control: The Case of Glossy Buckthorn in New Hampshire and Maine Forests," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304623, Agricultural and Applied Economics Association.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fem:femwpa:2009.33. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Alberto Prina Cerai The email address of this maintainer does not seem to be valid anymore. Please ask Alberto Prina Cerai to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/feemmit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.