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Discrimination in contests: a survey

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Abstract

The objective of this paper is to provide a comprehensive answer to some fundamental questions related to discrimination within the context of contests. For example, what forms of discrimination are possible? Can discrimination be justified? What mode of discrimination is expected? Does discrimination necessarily result in the elimination of polarization? How effective are the different modes of discrimination in inducing efforts (revenue)? How do the most widely studied contests based on an all-pay-auction and on a lottery compare under different modes of discrimination? Applying a contest-design approach, we examine four alternative types of discrimination that can be selected by a contest designer who maximizes the contestants’ efforts (his revenue). Our survey focuses on the leading principles of the separate and joint effective application of the alternative modes of direct, overt covert and head starts-discrimination that are assumed to be exercised under the widely studied family of (logit) contest success functions (CSFs). Whereas direct discrimination refers to differential taxation of the contested prize subject to a balanced-budget constraint, overt, covert and head starts-discrimination relate to structural discrimination that involves the parameters of the CSF. While the direct mode of discrimination is legally feasible, the structural modes of discrimination are more subtle and more difficult to implement and, sometimes, may even involve legal barriers.

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Notes

  1. Handicapping in sports and games is the practice of assigning advantage through scoring compensation or other advantage given to different contestants to equalize the chances of winning. The handicap system is used in many games and sports, including go, chess, croquet, golf, bowling, polo, basketball and track and field events.

  2. Consider, for example, a wooing game where several males compete for a single female. Efforts are the energy (time) spent by the males to woo the female. Efforts maximization is reasonable because it enables the female to evaluate the competing males’ ‘true potential’ in terms of genetic promise for off-springs and, in turn, choose the fittest one. In this case, the designer is either the female (which is also the contested prize) or the evolutionary process.

  3. In contrast to our study that focuses on a simultaneous game under complete information, there are papers that deal with a sequential contest setting and incomplete information. See, for example, Moldovanu and Sela (2006), Segev and Sela (2014a, b) and the literature mentioned in the latter strudy.

  4. A comparison between Tullock lotteries and an APA has been recently presented in Mealem and Nitzan (2015), assuming a given form of discrimination (see Table 4 in Sect. 10). The emphasis in the current paper is, however, different because it focuses on effort maximization under different forms of permissible discrimination and the family of logit CSFs.

  5. Specific cases of N-player contests will be dealt with in the sequel, e.g., in Sect. 10.1.

  6. Later on we relate to “head starts-discrimination” that was examined under APA and under a lottery. In the latter case the assumption is that in (1), \(\alpha =1\) and, therefore, the form of the contest success functions corresponding to this case is presented separately, see Eq. (5).

  7. For the most widely studied APA, \(\alpha =\infty \).

  8. Munster (2009) has recently generalized the axiomatic approach to group CSFs.

  9. The possibility of a balanced-budget constraint faced by the contest designer has not been dealt with in the contest literature. The possibility of caps on the contestants’ efforts has been examined, for example, by Che and Gale (1998) and Ujhelyi (2009).

  10. For a study of delegation of the rent-seeking activity by the contestants, see Baik and Kim (1997).

  11. Two such competing investment houses, Psagot and Ofek, were subsidiaries of the leading Bank in Israel, Bank Leumi. Another example of two such companies is Gadish and Tagmulim,that were two subsidiaries of another major Israeli bank, Bank Hapoalim.

  12. For head starts-discrimination, Franke et al. (2014b) deal with the comparison between the expected efforts of the contestants under APA and the lottery. This comparison is presented in the sequel. Our notation for head starts-discrimination differs from that of Franke et al. (2014b) in order to distinguish between this type of discrimination which is denoted by \(\beta \)and overt discrimination which is denoted by \(\delta \).

  13. For further discussion of the reason for this policy, see Case 8 in Table 2.

  14. Notice that the outcome of complete symmetry between the contestants is the equalization of the contestants’ winning probabilities. Under overt discrimination, this result is reached despite the fact that the contestants’ prize valuations differ, whereas under direct discrimination, this result is reached when the designer equates the contestants’ prize valuations.

  15. This will occur for \(1\le k<3^{0.75}\) when the optimal \(\alpha , \alpha >1\frac{1}{3}\), satisfies \(\left( {\alpha -1} \right) k^{\alpha }=1\), see Mealem and Nitzan (2012b).

  16. Studying the endogenous determination of the optimal prize, Runkel (2006) and Singh and Wittman (1998) consider a designer’s payoff function that depends on the performance of the contestants and on the difference in their winning probabilities (the closeness of the contest). This difference represents the uncertainty of the contest outcome that affects the interest it arouses and, in turn, the size of the contest audience. Dasgupta and Nti (1998) consider the endogenous determination of the contest success function, assuming that the designer’s objective function depends on aggregate efforts and on his own valuation of the prize that may induce him not to award the prize.

  17. As commonly assumed in the political economy literature, Grossman and Helpman (2001), and Persson and Tabellini (2000).

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Acknowledgments

We are indebted to the editor, an associate editor and anonymous referees for their most useful comments and suggestions.

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Authors and Affiliations

  1. Netanya Academic College, Netanya, Israel

    Yosef Mealem

  2. Bar-Ilan University, Ramat Gan, Israel

    Shmuel Nitzan

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  1. Yosef Mealem
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Correspondence to Shmuel Nitzan.

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Mealem, Y., Nitzan, S. Discrimination in contests: a survey. Rev Econ Design 20, 145–172 (2016). https://doi.org/10.1007/s10058-016-0186-0

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