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The optimal allocation of prizes in contests with costly entry

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  • Liu, Bin
  • Lu, Jingfeng

Abstract

Contestants often need to incur an opportunity cost to participate in the competition. In this paper, we accommodate costly entry and study the effort-maximizing prize allocation rule in a contest environment of all-pay auction with incomplete information as in Moldovanu and Sela (2001). As equilibrium entry can be stochastic, our analysis allows prize allocation rule to be contingent on the number of entrants. With free entry, Moldovanu and Sela establish the optimality of winner-take-all when effort cost function is linear or concave. Costly entry introduces a new trade-off between eliciting effort from entrants and encouraging entry of contestants, which might demand a more lenient optimal prize allocation rule. Surprisingly, we find that the optimality of winner-take-all is robust to costly entry when cost function is linear or concave. On the other hand, we provide examples to show that the new trade-off due to costly entry does make a difference to the optimal design when effort cost function is convex.

Suggested Citation

  • Liu, Bin & Lu, Jingfeng, 2019. "The optimal allocation of prizes in contests with costly entry," International Journal of Industrial Organization, Elsevier, vol. 66(C), pages 137-161.
    • Handle: RePEc:eee:indorg:v:66:y:2019:i:c:p:137-161
    DOI: 10.1016/j.ijindorg.2019.04.005
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    References listed on IDEAS

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    Cited by:

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    2. Whitmeyer, Mark, 2023. "Submission costs in risk-taking contests," Games and Economic Behavior, Elsevier, vol. 142(C), pages 101-112.
    3. Martin Grossmann, 2021. "Asymmetric Opportunities After an Unsuccessful Sports Career," Journal of Sports Economics, , vol. 22(5), pages 587-612, June.
    4. Ta, Chi L., 2024. "Do conservation contests work? An analysis of a large-scale energy competitive rebate program," Journal of Environmental Economics and Management, Elsevier, vol. 124(C).
    5. Shelegia, Sandro & Wilson, Chris M., 2022. "Costly participation and default allocations in all-pay contests," MPRA Paper 115027, University Library of Munich, Germany.
    6. Liu, Bin & Lu, Jingfeng, 2023. "Optimal orchestration of rewards and punishments in rank-order contests," Journal of Economic Theory, Elsevier, vol. 208(C).
    7. Sumit Goel, 2022. "Optimal grading contests," Papers 2205.05207, arXiv.org, revised Nov 2024.
    8. Mark Whitmeyer, 2021. "Submission Fees in Risk-Taking Contests," Papers 2108.13506, arXiv.org.

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    More about this item

    Keywords

    Optimal contest; Winner-Take-All; All-Pay auction; Costly entry; Incomplete information; Cross-Rank/scenario transfer;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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