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

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  • Mario Gilli
  • Andrea Sorrentino

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

  • Mario Gilli & Andrea Sorrentino, 2024. "Characterization of the Set of Equilibria in Max-Min Group Contests with Continuous Efforts and a Private Good Prize," Working Papers 541, University of Milano-Bicocca, Department of Economics.
    • Handle: RePEc:mib:wpaper:541
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. repec:wly:soecon:v:83:1:y:2016:p:105-125 is not listed on IDEAS
    5. Barbieri, Stefano & Topolyan, Iryna, 2024. "Correlated play in weakest-link and best-shot group contests," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    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.
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    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).

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    More about this item

    Keywords

    Group contests; sharing rules; indeterminacy.;
    All these keywords.

    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

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