The Optimal Allocation of Prizes in Contests

Abstract

We study a contest with multiple, nonidentical prizes. Participants are privately informed about a parameter (ability) affecting their costs of effort. The contestant with the highest effort wins the first prize, the contestant with the second-highest effort wins the second prize, and so on until all the prizes are allocated. The contest's designer maximizes expected effort. When cost functions are linear or concave in effort, it is optimal to allocate the entire prize sum to a single "first" prize. When cost functions are convex, several positive prizes may be optimal.

Influencing rent-seeking contests

“…6 It is well known that affine transformations of expected profits may allow for other interpretations of the asymmetries between players (for example, differences in talent or ability). 7 This objective function is widely employed in the literature on contest design, see e.g., Gradstein and Konrad (1999) and Moldovanu and Sela (2001).…”

“…1 Much recent work has focused on aspects of contest design, including variations in discriminatory power (Dasgupta and Nti 1998), simultaneous versus sequential (multi-stage) contests (Gradstein and Konrad 1999) and the number of prizes (Moldovanu and Sela 2001).…”

The optimal initial allocation of pollution permits: a relative performance approach

“…Another example of a double objective may be the regulation of two environmental targets, with one target being controlled by target pollutant permit market, and another target currently being unregulated-for example, emissions of CO 2 and a basket of other greenhouse gases. In any case, the secondary objective involves maximization of firms' aggregate activities, expenditures, or efforts (for a similar objective see for example Moldovanu and Sela 2001).…”

Going, Going, Gone! A Swift Tour of Auction Theory and its Applications

“…35 The following proposition gives the equilibrium properties of the all-pay auction in the SIPV model. 30 See, e.g., Che and Gale (1998a) and Moldovanu and Sela (2001). 31 See Matthews (1983) and Laffont and Robert (1996), respectively.…”