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Review of Industrial Organization

Erschienen in:

23.07.2018

Relative Performance Prizes and Dynamic Incentives in Best-of-N Contests

verfasst von: Xiandeng Jiang

Erschienen in: Review of Industrial Organization | Ausgabe 3/2018

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Abstract

This paper introduces a relative performance prize scheme to best-of-N contests. I develop a theoretical model of the best-of-N contest with intermediate prizes that are distributed based on the players’ relative performance. The model predicts that a relative performance prize scheme both increases the players’ level of effort in certain conditions and decreases the performance differential between the winner and the loser in the contest. Empirically, I investigate these theoretical predictions by employing a natural experiment in the group-stage matches of the FIVB (Fédération Internationale de Volleyball) World League and the FIVB World Grand Prix. The results indicate that the introduction of a relative performance prize scheme induces contest participants to intensify their efforts in certain conditions. However, this prize scheme may ultimately result in teams playing fewer sets in matches.

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In 2016, the Cleveland Cavaliers became the first team to win the championship after facing a 3-to-1 deficit.

Lazear and Rosen (1981) analyze and compare the efficiency of a relative performance compensation scheme in rank-order tournaments and other types of tournaments. Chan et al. (2009) study a linear relative performance prize scheme in a two-period contest. They find that the players continue exerting efforts in the second period regardless of the score differential at the end of the first period.

For instance, Formula 1 car races and the Tour de France reward their participants based on their relative performance; many public firms evaluate their CEOs based on relative performance (Jenter and Kanaan 2015). Moreover, lesser prizes for runner-up outcomes are common in: golf; tennis; marathons; and the Olympics (gold-silver-bronze).

This paper is related to other studies of dynamic contests that are theoretical (e.g., Clark and Riis 1998; Krishna and Morgan 1998; Moldovanu and Sela 2001; Lai and Matros 2006; Fu and Lu 2012; Schweinzer and Segev 2012) and empirical (e.g., McFall et al. 2009; Apesteguia and Palacios-Huerta 2010; Kocher et al. 2012; Neugart and Richiardi 2013).

Klumpp and Polborn (2006) apply this analysis to the US presidential nomination campaigns.

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The authors employ the Tullock contest success function to determine the participants’ winning probability in each round. In this type of success function, the discriminatory power basically measures the degree to which each player’s effort input affects his or her winning probability. A higher (lower) discriminatory power implies that a player’s effort plays a greater (smaller) role in his or her final chance of winning.

In this case, since Player i, the winner of Set 1, has already received an intermediate prize s, he will take the entire prize budget of v.

Each men’s team plays four matches against every opposing team in the group; each women’s team plays each opposing team in the group three times.

The team receives a monetary prize based on their final ranking. The allocation rules for the prize are not disclosed by the FIVB. However, the change in the number of monetary prizes over the sample period can be partially captured by the time trend variable.

According to the FIVB Official Volleyball Rules (http://www.fivb.org/EN/Refereeing-Rules), in the first four sets, in the case of a 24–24 tie play is continued until a two-point lead is achieved; in the fifth set, in the case of a 14–14 tie play is continued until a two-point lead is achieved.

The winning team wins the entire budget regardless of the final set score.

In this case, each team is given an intermediate prize s and the winning team wins the final prize \(\frac{1}{3}\).

Under the winner-take-all scheme, \(v=1\) and \(s=0\); under the relative performance prize scheme, \(v=\frac{1}{3}\) and \(s=\frac{1}{3}\).

The final prize under the old rule is 1; the final prize under the new rule is \(\frac{1}{3}\).

This sample includes 394 men’s matches and 286 women’s matches before the rule change, and 432 men’s matches and 252 women’s matches after the rule change.

I only keep the matches played since the third round of each season in order to capture a relative accurate ability for each team. I explain the reason in following paragraphs.

The number of sets played variable equals to three if the final set score is 3–0; it is four if the final set score is 3–1; and it is five if the final set score is 3–2.

This dummy variable takes 1 if the higher ability team plays on its home field and 0 otherwise.

The dummy variable takes 1 if the higher ability team is ahead before the set and 0 otherwise.

The dummy variable takes 1 if the set score is 2–0 after Set 2 and 0 otherwise.

I use the numerical value of each season year as the trend variable. For example, the trend variable for all the knockout-stage matches equals to 2008 in the year of 2008.

Please refer to Hahn et al. (2001), Guido and Lemieux (2008), and Lee and Lemieuxa (2010) for details of regression discontinuity design.

Gelman and Imbens (2014) suggest that using high-order polynomials of f(season) could lead to misleading results. Thus, I will also estimate the model using a linear function of f(season) in this paper.

The cutoff season is 2009 in the men’s league and 2010 in the women’s league.

I test the same hypothesis using the RDD setup with a season quartic polynomial and the results are still robust.

These estimates remain similar when the quartic polynomial of season is included.

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Titel: Relative Performance Prizes and Dynamic Incentives in Best-of-N Contests
verfasst von: Xiandeng Jiang
Publikationsdatum: 23.07.2018
Verlag: Springer US
Erschienen in: Review of Industrial Organization / Ausgabe 3/2018
Print ISSN: 0889-938X
Elektronische ISSN: 1573-7160
DOI: https://doi.org/10.1007/s11151-018-9646-8

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