On the optimal design of biased contests

Abstract

This paper explores the optimal design of biased contests. A designer imposes an identity‐dependent treatment on contestants that varies the balance of the playing field. A generalized lottery contest typically yields no closed‐form equilibrium solutions, which nullifies the usual implicit programming approach to optimal contest design and limits analysis to restricted settings. We propose an alternative approach that allows us to circumvent this difficulty and characterize the optimum in a general setting under a wide array of objective functions without solving for the equilibrium explicitly. Our technique applies to a broad array of contest design problems, and the analysis it enables generates novel insights into incentive provisions in contests and their optimal design. For instance, we demonstrate that the conventional wisdom of leveling the playing field, which is obtained in limited settings in previous studies, does not generally hold.

Competitive Balance: Information Disclosure and Discrimination in an Asymmetric Contest

“…The principal pursues a broad range of objectives that include among others total effort maximization and has two policy instruments − head starts and biases affecting effort productivities. Fu and Wu (2020) show that the multiplicative biases outperform head starts. Furthermore, in the contest designed to obtain maximal effort, the contestants' winning probabilities can be non-monotone with respect to the rankings of their prize valuations.…”

“…With more than two players, favoring a player also affects the strategic interaction among other players and the composite effect can be complex. Fu and Wu (2020) consider the design problem for a principal in an n-player lottery contest with heterogeneous contestants differing in their prize valuations. The principal pursues a broad range of objectives that include among others total effort maximization and has two policy instruments − head starts and biases affecting effort productivities.…”

“…Furthermore, in the contest designed to obtain maximal effort, the contestants' winning probabilities can be non-monotone with respect to the rankings of their prize valuations. Unlike Franke et al (2013) and Fu and Wu (2020), we limit our attention to two-player contest under asymmetric information and allow the principal to choose both the extent of information disclosure and the bias affecting effort productivity.…”

Competitive Balance: Information Disclosure and Discrimination in an Asymmetric Contest

“…For the two-player case, Franke (2012) shows how biasing the effort s optimally in relation to competitors' cost of effort (or equivalently prize valuation) leads to maximal contest effort. 12 Fu and Wu (2020) show that multiplicative biases outperform additive heads starts in an n -player lottery contest with heterogeneous contestants differing in their prize valuations. The principal pursues a broad range of objectives, including total effort maximization.…”

Conflicts with Momentum

“…Our work is most similar to contest models that emphasize "head starts" in the sense of giving one party or another a cost advantage of some kind, as studied in [1][2][3]. These papers, however, focus in particular on the optimal setting of cost advantages (or disadvantages) in order to maximize effort expenditures by contestants, as if set by the contest designer.…”