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Stochastic stability in best shot network games

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  • Boncinelli, Leonardo
  • Pin, Paolo

Abstract

The best shot game applied to networks is a discrete model of many processes of contribution to local public goods. It generally has a wide multiplicity of equilibria that we refine through stochastic stability. We show that, depending on how we define perturbations – i.e., possible mistakes that agents make – we can obtain very different sets of stochastically stable states. In particular and non-trivially, if we assume that the only possible source of error is that of a contributing agent that stops doing so, then the only stochastically stable states are Nash equilibria with the largest contribution.

Suggested Citation

  • Boncinelli, Leonardo & Pin, Paolo, 2012. "Stochastic stability in best shot network games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 538-554.
  • Handle: RePEc:eee:gamebe:v:75:y:2012:i:2:p:538-554
    DOI: 10.1016/j.geb.2012.03.001
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Boris van Leeuwen & Theo Offerman & Arthur Schram, 2013. "Superstars need Social Benefits: An Experiment on Network Formation," Tinbergen Institute Discussion Papers 13-112/I, Tinbergen Institute.
    2. Dunia Lopez-Pintado, 2016. "Influence networks and public goods," UMASS Amherst Economics Working Papers 2016-12, University of Massachusetts Amherst, Department of Economics.
    3. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications, Elsevier.
    4. Offerman, Theo & Schram, Arthur & Van Leeuwen, Boris, 2014. "Competition for status creates superstars: An experiment on public good provision and network formation," IAST Working Papers 14-16, Institute for Advanced Study in Toulouse (IAST).
    5. Charness, Gary & Feri, Francesco & Meléndez-Jiménez, Miguel A. & Sutter, Matthias, 2012. "Equilibrium Selection in Experimental Games on Networks," University of California at Santa Barbara, Economics Working Paper Series qt51v6w9hd, Department of Economics, UC Santa Barbara.
    6. Dunia López-Pintado, 2015. "Influence Networks and Public Goods," Working Papers 15.04, Universidad Pablo de Olavide, Department of Economics.
    7. Kukushkin, Nikolai S., 2017. "Strong Nash equilibrium in games with common and complementary local utilities," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 1-12.
    8. repec:spr:series:v:8:y:2017:i:1:d:10.1007_s13209-016-0152-7 is not listed on IDEAS
    9. Gary Charness & Francesco Feri & Miguel A. Meléndez‐Jiménez & Matthias Sutter, 2014. "Experimental Games on Networks: Underpinnings of Behavior and Equilibrium Selection," Econometrica, Econometric Society, vol. 82, pages 1615-1670, September.
    10. Yann Bramoullé & Rachel Kranton, 2015. "Games Played on Networks," Working Papers halshs-01180657, HAL.
    11. Nikolai Kukushkin, 2015. "The single crossing conditions for incomplete preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 225-251, February.
    12. Boncinelli, Leonardo & Pin, Paolo, 2014. "Efficiency and Stability in a Process of Teams Formation," MPRA Paper 56356, University Library of Munich, Germany.
    13. Cui, Zhiwei & Wang, Shouyang & Zhang, Jin & Zu, Lei, 2013. "Stochastic stability in one-way flow networks," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 410-421.

    More about this item

    Keywords

    Networks; Best shot game; Stochastic stability;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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