IDEAS home Printed from https://ideas.repec.org/p/ags/feemwp/344221.html
   My bibliography  Save this paper

Characterization of the Set of Equilibria in Max-Min Group Contests with Continuous Efforts and a Private Good Prize

Author

Listed:
  • Gilli, Mario
  • Sorrentino, Andrea

Abstract

We characterise the set of equilibria in a deterministic group contest with the weakest-link impact function, continuous efforts and a private good prize, complementing the results obtained by Chowdhury et al. (2016). We consider a two-stages two-groups model, where in the first stage the agents simultaneously choose the sharing rule, while in the second stage they choose efforts. Despite the existence of within-group symmetric Nash equilibria in pure strategies in the effort stage, there are combinations of possible sharing rules such that no pure strategy effort equilibria exist, hence for these sharing rules, the continuation payoffs are not defined, so that there exist no subgame perfect Nash equilibria in pure stragies. However, limiting ourselves to the restricted sharing rules case, we are able to state that there are continua of subgame perfect equilibria. In this case, by additional restrictions on the effort levels of each class of effort equilibria, we are able to computationally characterise the set of subgame perfect equilibria in pure strategies.

Suggested Citation

  • Gilli, Mario & Sorrentino, Andrea, 2024. "Characterization of the Set of Equilibria in Max-Min Group Contests with Continuous Efforts and a Private Good Prize," FEEM Working Papers 344221, Fondazione Eni Enrico Mattei (FEEM).
    • Handle: RePEc:ags:feemwp:344221
    DOI: 10.22004/ag.econ.344221
    as

    Download full text from publisher

    File URL: https://ageconsearch.umn.edu/record/344221/files/NDL2024-21.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.22004/ag.econ.344221?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. repec:wly:soecon:v:83:1:y:2016:p:105-125 is not listed on IDEAS
    2. Subhasish M. Chowdhury & Dongryul Lee & Iryna Topolyan, 2016. "The Max‐Min Group Contest: Weakest‐link (Group) All‐Pay Auction," Southern Economic Journal, John Wiley & Sons, vol. 83(1), pages 105-125, July.
    3. Barbieri, Stefano & Topolyan, Iryna, 2024. "Correlated play in weakest-link and best-shot group contests," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    4. Kolmar, Martin & Rommeswinkel, Hendrik, 2013. "Contests with group-specific public goods and complementarities in efforts," Journal of Economic Behavior & Organization, Elsevier, vol. 89(C), pages 9-22.
    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.
    6. Lee, Dongryul, 2012. "Weakest-link contests with group-specific public good prizes," European Journal of Political Economy, Elsevier, vol. 28(2), pages 238-248.
    7. Subhasish M. Chowdhury & Iryna Topolyan, 2016. "The Attack-And-Defense Group Contests: Best Shot Versus Weakest Link," Economic Inquiry, Western Economic Association International, vol. 54(1), pages 548-557, January.
    8. Roman M. Sheremeta, 2011. "Perfect-Substitutes, Best-Shot, and Weakest-Link Contests between Groups," Korean Economic Review, Korean Economic Association, vol. 27, pages 5-32.
    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. Gilli, Mario & Sorrentino, Andrea, 2024. "The Set of Equilibria in Max-Min Two Groups Contests with Binary Actions and a Private Good Prize," FEEM Working Papers 343494, Fondazione Eni Enrico Mattei (FEEM).

    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. 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..
    2. Mario Gilli & Andrea Sorrentino, 2024. "The Set of Equilibria in Max-Min Two Groups Contests with Binary Actions and a Private Good Prize," Working Papers 539, University of Milano-Bicocca, Department of Economics.
    3. Subhasish M. Chowdhury & Dongryul Lee & Iryna Topolyan, 2016. "The Max‐Min Group Contest: Weakest‐link (Group) All‐Pay Auction," Southern Economic Journal, John Wiley & Sons, vol. 83(1), pages 105-125, July.
    4. Dongryul Lee & Joon Song, 2019. "Optimal Team Contests to Induce More Efforts," Journal of Sports Economics, , vol. 20(3), pages 448-476, April.
    5. Subhasish M. Chowdhury & Iryna Topolyan, 2016. "Best-shot versus weakest-link in political lobbying: an application of group all-pay auction," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 959-971, December.
    6. Martin Kolmar & Hendrik Rommeswinkel, 2020. "Group size and group success in conflicts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 777-822, December.
    7. Dan Kovenock & Brian Roberson, 2018. "The Optimal Defense Of Networks Of Targets," Economic Inquiry, Western Economic Association International, vol. 56(4), pages 2195-2211, October.
    8. Roman M. Sheremeta, 2018. "Behavior In Group Contests: A Review Of Experimental Research," Journal of Economic Surveys, Wiley Blackwell, vol. 32(3), pages 683-704, July.
    9. Chowdhury, Subhasish & Mukherjee, Anwesha & Sheremeta, Roman, 2021. "In-group versus Out-group Preferences in Intergroup Conflict: An Experiment," MPRA Paper 105690, University Library of Munich, Germany.
    10. Dongryul Lee & Pilwon Kim, 2022. "Group formation in a dominance-seeking contest," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 39-68, January.
    11. Stefano Barbieri & David Malueg & Iryna Topolyan, 2014. "The best-shot all-pay (group) auction with complete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 603-640, November.
    12. Timothy N. Cason & Roman M. Sheremeta & Jingjing Zhang, 2017. "Asymmetric and endogenous within-group communication in competitive coordination games," Experimental Economics, Springer;Economic Science Association, vol. 20(4), pages 946-972, December.
    13. Cason, Timothy N. & Sheremeta, Roman M. & Zhang, Jingjing, 2012. "Communication and efficiency in competitive coordination games," Games and Economic Behavior, Elsevier, vol. 76(1), pages 26-43.
    14. Timothy N. Cason & Roman M. Sheremeta & Jingjing Zhang, 2015. "Asymmetric and Endogenous Communication in Competition between Groups," Working Papers 15-01, Chapman University, Economic Science Institute.
    15. Brookins, Philip & Jindapon, Paan, 2021. "Risk preference heterogeneity in group contests," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    16. 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.
    17. Subhasish M. Chowdhury & Iryna Topolyan, 2016. "The Attack-And-Defense Group Contests: Best Shot Versus Weakest Link," Economic Inquiry, Western Economic Association International, vol. 54(1), pages 548-557, January.
    18. Jay Pil Choi & Subhasish M. Chowdhury & Jaesoo Kim, 2016. "Group Contests with Internal Conflict and Power Asymmetry," Scandinavian Journal of Economics, Wiley Blackwell, vol. 118(4), pages 816-840, October.
    19. Stefano Barbieri, 2023. "Complementarity and information in collective action," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 167-206, January.
    20. Subhasish M. Chowdhury & Iryna Topolyan, 2015. "The Group All-Pay Auction with Heterogeneous Impact Functions," University of East Anglia Applied and Financial Economics Working Paper Series 069, School of Economics, University of East Anglia, Norwich, UK..

    More about this item

    Keywords

    Research Methods/ Statistical Methods;

    JEL classification:

    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:ags:feemwp:344221. 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: AgEcon Search (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.