Incentives in Tournaments

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• Incentives in Tournaments
• with Heterogeneous Agents
• Empirical Evidence from the German Bundesliga
• Bernd Frick and Joachim Prinz
• University of Paderborn
• bernd.frick_at_notes.upb.de
• joachim.prinz_at_wiwi.uni-paderborn.de
• Oliver Gürtler
• University of Bonn
• oliver.guertler_at_uni-bonn.de

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Structure of the Presentation

• Motivation
• Related Literature
• The Model
• 4. Data and Hypothesis
• Estimation and Empirical Findings
• Summary and Implications

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1. Motivation (I)

• Tournaments are an important element of firms
  incentive systems
• Promotion tournaments are used to identify the
  most talented employee(s)
• Bonus pools are offered to motivate the most
  productive em-ployee(s).
• Theory suggests that tournaments can be effective
  only if the con-testants are homogeneous. In
  tournaments with heterogeneous par-ticipants the
  underdog will soon recognize that he has no
  chance to win and will, therefore, reduce his
  effort. The favorites best respon-se is to
  reduce his effort, too. Thus, the incentive
  effects of tourna-ments are likely to
  disappear

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1. Motivation (II)

• The design of tournaments
• prizes are fixed in advance and independent of
  absolute performan-ce
• - a player receives the winners prize not by
  being good, but by being better than the other
  player
• the level of effort of each player depends on the
  size of the potential increase in his wage
• since the optimal amount of effort is not
  infinite, there is a limit to the prize spread.
• The average prize money must be high enough to
  attract contest-ants to enter the tournament in
  the first place

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1. Motivation (III)

• larger prize spreads not only induce higher
  effort levels, but may also result in a rat
  race
• collusion is less likely, if the number of
  contestants is high as an agreement to slack off
  is difficult to enforce
• the higher the noise in the tournament (luck,
  production uncertain-ty and measurement error),
  the lower the level of effort
• the more important luck is in determining the
  winner, the larger the spread has to be
• tournaments serve a sorting function as well as
  an incentive function

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1. Motivation (IV)

• advantage of using relative performance as
  measure of effort
• lower measurement costs
• elimination of the effect of luck on reward
• Problem to be addressed in our empirical analysis
• efforts suffer when heterogeneous contestants
  compete with each other. Effort has the largest
  effect on changing the probability of winning
  when the contestants are of similar ability. If
  ability differs among contestants, then both the
  less able and the more able tend to slack off.

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1. Motivation (V)

• to maintain high levels of effort, it is
  important to group contestants so that, at least
  at the outset, participants feel they are (more
  or less) evenly matched with those against whom
  they will directly compete for the tournament
  prize.
• when contestants are (too) heterogeneous not even
  a highly skewed prize money distribution will
  motivate well, because contestants who feel that
  they have no chance of winning the tournament
  will give up early.
• - Our paper is the first to test this hypothesis
  in the context of a pro-fessional team sports
  league, the German Bundesliga.

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1. Motivation (VI)

• It is difficult to observe the effects of
  tournament-like pay structures on effort because
  in cases where tournaments are used, neither
  effort nor output is easily observed. If effort
  or output could be observed easily, then the case
  for using a relative performance-based incentive
  scheme would be diminished. There is, however,
  one arena in which output is easily measured and
  in which the tournament pay structure is explicit
  professional sports (Lazear 1998 241).

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2. Related Literature
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3. The Model (I)

• N
• (1) yi S eij ai ei
• i1
• (2) Ui U(Ii) - C(ei)
• Prob S e1j a1 e1 gt S e2j a2 e2
• Prob e2 - e1 lt S e1j - S e2j a1 - a2
• G(S e1 - S e2 a1 - a2)

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3. The Model (II)

• EU1j U(w2) G(S e1j - S e2j a1 - a2) (U(w1)
  (U(w2)) C(e1)
• and
• (5) EU2j U(w2) 1 - G (S e1j - S e2j a1 -
  a2) (U(w1) - U(w2)) - C(e2j)

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3. The Model (III)

• dEU1j
• (6) ________ g (S e1j - S e2j a1 - a2)
  (U(w1) - U(w2)) - C(e1j) 0
• de1j
• dEU2j
• (7) ________ g (S e1j - S e2j a1 - a2)
  (U(w1) - U(w2)) - C(e2j) 0
• de2j
• (8) g (a1 a2) (U(w1) U(w2)) C(e)

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3. The Model (IV)

• Result 1
• The optimal level of effort of both contestants
  is strictly decreasing in a1 - a2

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Figure 1Talent Difference and Optimal Effort
Level
Effort Level
Talent Difference
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4. Data and Hypothesis (I)

• 756 matches played in the seasons 1998/99
  (n144), 1999/2000 (n306) and 2000/01 (n306)
• Match and referee characteristics as well as
  betting odds (Oddset)
• - age of referee
• - body mass index
• - FIFA-referee (0no 1yes)
• - goals scored by home and away team
• - attendance
• - score after 45 minutes

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4. Data and Hypothesis (II)

• We use two different, yet related measures of
  heterogeneity of the contestants
• HET1 ODDS_H ODDS_A
• HET2 ODDS_H2 - ODDS_A2
• The larger the heterogeneity between the two
  competing teams (HET), the smaller the
  intensity of the match, i.e. the smaller the
  number of cards (CARDS).

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Figure 2Number of Disciplinary Sanctions (I)
Number of Matches
Number of Yellow Cards and Total Number of Cards
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Figure 3Number of Disciplinary Sanctions (II)
Number of Matches
Number of Yellow / Red and Red Cards
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Figure 4Kernel Density Estimate of HET1 and HET2
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5. Estimation and Empirical Findings (I)

• The model is of the following general form
• CARDS a0 a1 AGE a2 AGE2 a3 BMI a4 FIFA
  
• a6 H_G a7 A_G a8 ATT a9 ATT2
  a10 HTS
• a11 DER a12 HET e
• Count data model controlling for unobserved
  referee-specific effects (Negbin Model with
  Random and Fixed Effects).

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Table 1Intensity Measures
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Table 2Control Variables
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Table 3Betting Odds
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5. Estimation and Empirical Findings (II)
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5. Estimation and Empirical Findings (III)
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6. Summary and Implications (I)

• Using a unique data set from the top tier in
  German professional football we demonstrate that
  the effort levels of the two teams in a single
  match are significantly lower when the teams are
  heteroge-neous.
• Our measure of match intensity is the number of
  disciplinary sanc-tions, the measure of
  heterogeneity is the (squared) difference in the
  respective betting odds.
• - So far, we have looked at destructive efforts
  only. In further re-search we will, of course,
  also look at constructive efforts.

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6. Summary and Implications (II)

• Next steps include
• International comparison with data from the other
  four top lea-gues in Europe (England, Italy,
  France and Spain)
• Adding controls for the market values of the
  teams at the start of the respective season.

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Literature

• Chevalier, J., and G. Ellison (1997) Risk Taking
  by Mutual Funds as a Respon-se to Incentives.
  Journal of Political Economy, 105, pp. 1167-1200
• Clark, D. and C. Riis (2001) Rank-Order
  Tournaments and Selection. Journal of Economics,
  73, pp. 167-191
• Kräkel, M. and D. Sliwka (2004) Risk Taking in
  Asymmetric Tournaments. Ger-man Economic Review,
  5, pp. 103-116
• Lazear, E. (1998) Personnel Economics for
  Managers, New York Wiley
• Lazear, E. and S. Rosen (1981) Rank-Order
  Tournaments as Optimum Labor Contracts. Journal
  of Political Economy, 89, pp. 841-864
• Schotter, A. and K. Weigelt (1992) Asymmetric
  Tournaments, Equal Opportu-nity Laws, and
  Affirmative Action Some Experimental Results,
  in Quarterly Journal of Economics, 107, pp.
  511-539