Tournament Winner Proportion and its Effect on Effort: An Investigation of the Underlying Psychological Mechanisms

Abstract

This study investigates the effects of the psychological mechanisms activated by different proportions of tournament winners on effort. Using a real-effort experiment that allows the evolution of social comparison, which is central to our theory, we show that firms can increase employee effort (and performance) by increasing the proportion of winners. Based on a causal model, we generate evidence for our theory that this effect is driven by relative performance concerns and bonus concerns, both of which depend on the proportion of tournament winners. In addition, we find that, over time, the change in effort is more negative the lower the proportion of winners. This effect is driven by the different behaviors of winners and losers in a previous tournament.

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Corrigendum

Acknowledgements

We thank Victor Maas (associate editor), two anonymous reviewers, Corinna Ewelt-Knauer, Lynn Hannan, Anja Schwering, Ivo Tafkov, Kristy Towry, and the participants and discussants at the University of Münster workshop; the 2013 Accounting, Behavior and Organizations Research Conference; the 2014 Annual Conference for Management Accounting Research; and the 37th European Accounting Association Annual Congress for their helpful comments and suggestions.

ORCID

Thorsten Knauer http://orcid.org/0000-0002-2734-9996

Friedrich Sommer http://orcid.org/0000-0002-7697-2864

Arnt Wöhrmann http://orcid.org/0000-0003-4157-5401

Notes

1 Table 1 in Harbring and Irlenbusch (2003) presents theoretical predictions of equilibrium effort for various tournament designs. The authors predict a positive effect of the proportion of winners on effort from low to medium but no further increase for a high proportion. In contrast to their prediction, they find a continuous increase in effort and assume that this increase is due to lower-than-predicted effort levels in the medium treatment.

2 To test models that require perfectly homogeneous contestants, the aforementioned studies employ chosen-effort experiments. The use of chosen-effort rules out the possibility that the results are affected by social comparison (Festinger, 1954). Hence, in a setting which allows social comparison to evolve, this result does not necessarily hold.

3 The second component of expectancy theory is instrumentality. Instrumentality relates to factors such as trust in leadership, control, and policy type, all of which affect employees’ perceptions of whether they will receive a reward if they achieve their performance expectations (Vroom, 1964). Our intention is not to vary the instrumentality level; thus, we hold the instrumentality component constant. The third input factor considered by expectancy theory is the valence of the outcome, that is, the attractiveness of the winner prize compared with the loser prize (Birnberg, Luft, & Shields, 2007). In our research setting, we also hold the bonus pool constant. Therefore, when the proportion of winners increases, the value of the winner and loser prizes must decrease. However, we hold the difference between the winner and loser prizes, the prize spread, constant. In other words, although the winner prize is lower when there are more winners, its relative attractiveness in comparison with the loser prize does not change. Hence, the effects predicted by expectancy theory depend only on the expectation regarding the probability of winning.

4 We also strive to hold the tournament type (a multiple-prize tournament instead of a multiple- and single-prize tournament) constant. Therefore, we framed the experiment in a way that all participants perceived that they could win a bonus. However, we acknowledge that the condition of the low proportion of winners could be interpreted as a single-prize tournament if participants perceive the loser bonus as a fixed income.

5 Note that the tournaments are a series of single contests, since participation in subsequent rounds does not depend on prior performance. Therefore, the theory of multiple tournaments does not apply (Sisak, 2009).

6 Although tournaments have the advantage over piece-rate contracts that they control for common uncertainty regarding employees’ performance that is shared among the agents (Lazear & Rosen, 1981), this uncertainty is not central to our theory. Our theory relates to social comparison within a tournament rather than across tournaments. Therefore, we follow Hannan et al. (2013b) and hold the common uncertainty at zero to simplify the experiment.

7 While the number of college-level math classes is an objective and absolute measure, participants’ perception of their general problem-solving skills is a relative and subjective measure. Because problem-solving skills are, on the one hand, difficult to measure and, on the other hand, not perfectly reflected by, for example, math background, we decided to use a relative measure. One advantage of this measure is that we can rule out the possibility that participants in one treatment group show less effort than those in other treatment groups because significantly more participants in a group felt that their problem-solving skills were inferior.

8 The subjects also learned their relative rank (1 (best)–6 (worst)), but they were not informed about the ranks of the other participants. We informed the participants about their ranking position solely for experimental control to hold feedback constant across conditions because research shows that relative performance information in tournaments affects behavior (e.g. Hannan et al., 2008; Newman & Tafkov, 2014).

9 The results remain inferentially identical when the dependency in subsequent observations for the same subject is considered in a repeated-measures ANOVA (F = 8.03, p < .01, two-tailed).

10 For example, Hannan et al. (2013) use such contrast weights for a similar analysis. Our results are inferentially identical if we use alternative contrast weights for the low, medium, and high group, that is −2, −1, and +3 (F = 12.78, p < .01, two-tailed) or −5, −1, and +6 (F = 14.74, p < .01, two-tailed).

11 Our results are inferentially identical (untabulated) if we use initial effort (time spent solving the mathematical problems in the first tournament) or performance as the dependent variable.

12 Tafkov (2013) shows that the multiplication task employed is appropriate for a strong relation between social comparison and competitive behavior for three reasons: First, the participants were aware that the multiplication problems are identical for all group members. Second, the participants were recruited from a group of business students with similar backgrounds. Third, Tafkov (2013) argues that, to fulfill the last requirement for a strong relation between social comparison and competitive behavior as posited by Festinger (1954), contestants must believe that performance on the experimental task is informative about their general problem-solving abilities and that general problem-solving abilities matter. Tafkov (2013) indeed finds that the third condition is met for the multiplication task. Applying the same procedure, we also find that all requirements for this condition are met. First, the participants indicated on a 7-point Likert scale the extent to which they think that general problem-solving skills are important (1 (not at all) – 7 (to a great degree)) for succeeding in business (business importance) and in life (life importance). We find that the participants’ mean response for business importance (life importance) equals 6.11 (5.52) and significantly differs from the midpoint of 4, with t = 21.83 and p < .01 (two-tailed) (t = 11.18 and p < .01 (two-tailed)). The participants were also asked to indicate the extent to which they agree that not only mechanical skills but also general problem-solving ability is required for the experimental task. The participants’ mean response is 4.61 and is thus again significantly greater than the midpoint of 4 (t = 3.37 and p < .01 (two-tailed)). In sum, we conclude that the participants believe that general problem-solving ability is important and that the experimental task requires this ability.

13 The good model fit for the causal model for H1 (effort and performance in the first round) is supported by a chi-squared test of the covariance matrix implied by the model – χ = 5.54, p = .24 (χ = 3.48, p = .48) – a Tucker–Lewis index of 0.97 (1.01), and an incremental fit index of 0.99 (1.01).

14 We calculate the p-value of the indirect effect by using a bootstrap approximation of bias-corrected confidence intervals, as suggested by Shrout and Bolger (2002).

15 We report Type III SS in Table 5, Panel A, because the four cells are unbalanced. There are 5 observations in the low × winner group, 5 observations in the high × loser group, and 25 observations in each of the two other cells.

16 We acknowledge that our findings may be limited to situations which do not entail extremely large or extremely low proportions of winners. This might be the case if the size of the tournament is substantially increased. In such a situation, the probability of losing (winning) is so low when the proportion of winners is relatively high (low) that both too few and too many winners can be detrimental to the overall effort exerted in a tournament, the former owing to giving up and the latter owing to complacency. Rather, our theory applies to situations where social comparison matters to employees and where the probability of winning is neither miniscule nor substantial.

Additional information

Funding

This work was supported by the Dr. Werner Jackstädt-Stiftung.