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Contest divisioning

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Abstract

In this paper, we ask a fundamental design question in the theory of contests: Should contestants and reward money be pooled into a single grand contest, or should they be divided into parallel subcontests? We theoretically explore optimal divisioning using Tullock’s lottery contest framework and compare the performance, i.e., total effort generated, of the grand contest to the performance of contest divisioning based on players’ ability or risk attitude. When all players are risk neutral, contest divisioning is never optimal. However, given that players are heterogeneous in either ability or risk attitude, we find that contest divisioning is optimal when the degrees of absolute risk aversion are sufficiently large. Importantly, our results support the widespread use of divisioning seen in practice.

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Notes

  1. For recent comprehensive reviews of the theoretical contest literature see Vojnović (2015), Corchón and Serena (2018) and Fu and Zenan (2019).

  2. The effects of heterogeneity on contestants’ effort is ultimately an empirical question. Theoretically, increasing heterogeneity has an ambiguous affect on contest behavior (see, e.g., Ryvkin 2013; Drugov and Ryvkin 2022).

  3. We summarize the literature using a Tullock-style lottery CSF. Divisioning has received some attention in other settings assuming risk neutral players. See Moldovanu and Sela (2006) for private information all-pay auctions (Moldovanu and Sela 2001) and Fang et al. (2020) and Xiao (2019) for public information all-pay auctions.

  4. Similar existence and uniqueness arguments are applied to any combination of risk and ability heterogeneity discussed below.

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Authors and Affiliations

  1. Department of Economics, University of South Carolina, Columbia, SC, 29208, USA

    Philip Brookins

  2. Department of Economics, Finance and Legal Studies, University of Alabama, Tuscaloosa, AL, 35487, USA

    Paan Jindapon

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  1. Philip Brookins
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  2. Paan Jindapon
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Correspondence to Philip Brookins.

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We thank participants of the \(7^{\text {th}}\) Annual Conference on Contests: Theory and Evidence, two anonymous reviewers, and the Associate Editor for helpful comments.

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Brookins, P., Jindapon, P. Contest divisioning. Rev Econ Design (2022). https://doi.org/10.1007/s10058-022-00311-9

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