SELF-SELECTION AND THE EFFICIENCY OF TOURNAMENTS

The literature has shown that the overall efficiency of exogenously imposed tournaments is reduced by a high variance in performance. This article reports results from an experiment analyzing whether allowing subjects to self-select into different payment schemes is reducing the variability of performance in tournaments. We show that when the subjects choose to enter a tournament instead of a piece-rate payment scheme, the average effort is higher and the between-subject variance is substantially lower than when the same payment scheme is imposed. Mainly based on risk aversion, sorting is efficiency enhancing since it increases the homogeneity of the contestants . ( JEL M52, J33, J31, C81, C91)     

THE OPTIMAL ALLOCATION OF PRIZES IN TOURNAMENTS OF HETEROGENEOUS AGENTS

Tournaments are widely used in organizations, explicitly or implicitly, to reward the best‐performing employees, for example, by promotion or bonuses, and/or to penalize the worst‐performing employees, for example, by demotion, withholding bonuses, or unfavorable job assignments. These incentive schemes can be interpreted as various prize allocations based on the employees' relative performance. While the optimal prize allocation in tournaments of symmetric agents is relatively well understood, little is known about the impact of the allocation of prizes on the effectiveness of tournament incentive schemes for heterogeneous agents. We show that while multiple prize allocation rules are equivalent when agents are symmetric in their ability, the equivalence is broken in the presence of heterogeneity. Under a wide range of conditions, loser‐prize tournaments, that is, tournaments that award a low prize to relatively few bottom performers, are optimal for the firm. The reason is that low‐ability agents are discouraged less in such tournaments, as compared to winner‐prize tournaments awarding a high prize to few top performers, and hence can be compensated less to meet their participation constraints. (JEL M52, J33, J24)     

A new old solution for weak tournaments

This article uncovers dynamic properties of the von Neumann–Morgenstern solution in weak tournaments and majoritarian games. We propose a new procedure for the construction of choice sets from weak tournaments, based on dynamic stability criteria. The idea is to analyze dynamic versions of tournament games. The exploration of a specific class of Markov perfect equilibria in these “dynamic tournament games” yields a new solution concept for weak tournaments—the A-stable set. The alternatives in an A-stable set constitute persistent, long-run policy outcomes in the corresponding dynamic tournament games. We find that, in any weak tournament, the class of A-stable sets coincides with that of von Neumann–Morgenstern stable sets.     

A DESIGNER'S CHOICE BETWEEN SINGLE‐PRIZE AND PARALLEL TOURNAMENTS

In this article, I theoretically and experimentally compare a designer's profits from two tournament designs. The first design is a standard winner‐take‐all tournament with a single prize. The second design features two winner‐take‐all (parallel) tournaments with different prizes where individuals choose which tournament to enter before competing. I develop a simple model that illustrates how the relative performances of these designs change as contestants' abilities differ. The theoretical model shows that the designer's profit is higher (lower) in the parallel tournament when contestants' abilities differ greatly (are similar). I complement these findings with experimental evidence. The experiments show that the parallel tournament is more profitable under high heterogeneity, whereas under low heterogeneity, the designer is better off with the single‐prize tournament. Furthermore, high‐ability agents under‐participate and low‐ability agents over‐participate in the high‐prize tournament relative to the theoretical prediction. (JEL C72, D82, J33, M51, M52)     

Wage Inequality and Performance in Nonprofit and For‐Profit Organizations

This article examines the effects of several forms of wage inequality on service quality and employee effort. We suggest that two popular theories, tournament and fair wage/equity, are not necessarily competing. Each theory accurately describes aspects of employee behavior, but because of sectoral differences in organizational objectives and employee attitudes, tournament theory's predictions are relatively stronger in the for‐profit sector, while fair wage/equity theory's predictions are relatively stronger in the nonprofit sector. Using an employer–employee matched data set of nursing homes linked to a federal regulatory database and a resident survey, we found that ownership moderates the relationship between wage inequality and service quality. Although wage inequality positively affects service quality in the for‐profit sector, the reverse is true among nonprofit organizations. We also found that overall wage inequality in the workplace has a more pronounced influence on employee discretionary effort than does the employee's place in the distribution of wages.     

INTERMEDIATE INFORMATION,LOSS AVERSION,AND EFFORT: EMPIRICAL EVIDENCE

The present article empirically explores the impact of intermediate information on contestants' effort. Data involving substituted soccer players of the German Bundesliga indicate only weak evidence of a negative effect of ex ante heterogeneity on effort; in contrast, intermediate information, measured by goal difference at the time of substitution, significantly affects effort. Players exert the greatest effort when their team is leading by one goal and reduce their effort when it is trailing. When intermediate information suggests the contest is already decided, players from both teams reduce effort. This behavior is in line with loss aversion, such that players weight potential losses more than potential gains and adjust their effort accordingly. (JEL Z22, J41, M54)     

A PRIMER ON CARDINAL VERSUS ORDINAL TOURNAMENTS

This paper fills in a gap in the tournament literature by developing a framework that can be used to analyze both cardinal and ordinal tournaments, as well as piece rates. The analysis aims to obtain a Pareto ranking of cardinal versus ordinal tournaments, which is an open question in the literature. The analysis shows that, surprisingly, cardinal tournaments are superior to ordinal tournaments. The rationale is that, by utilizing all the available information more efficiently, cardinal tournaments allow the principal to implement higher power incentives, which makes them superior even though they restrict the form of the contract more than ordinal tournaments. (JEL D82, D21)     

Affirmative Action Can Increase Effort

Previous theoretical work examining labor tournaments concluded that an affirmative action program will always reduce the effort supplied by agents, thereby reducing output and profit for the tournament administrator; however, experimental results sometime contradict this conclusion. In the context of a labor tournament I demonstrate that there exists an affirmative action program that induces both types of agents to provide greater effort. In some instances the effort maximizing affirmative action program will also give both types of agents an equal chance of winning the tournament.

Choice set,relative income,and inequity aversion: An experimental investigation

Inequity aversion preference has been widely applied in interpretations of various economic behaviors. A rapidly growing literature has been attempting to measure the strength of inequity aversion preferences as accurately as possible. We vary two factors that might affect the accuracy of the measurement of inequity aversion preference, i.e., choice sets with different underlying inequity aversion strength ranges and with different relative income inequities while absolute income inequities remain fixed. We find that unidirectional changes in the choice sets for disadvantageous and advantageous inequity aversion preferences significantly bias the measured strength of both preferences in the same directions of the changes and that the variance in inequity aversion increases with the range of choice sets. Moreover, a decrease in relative income inequity raises the measured strength of advantageous inequity aversion but does not affect disadvantageous inequity aversion preference. Our results suggest controlling for choice sets and relative income inequity between players to improve the measurement accuracy of inequity aversion preference.     

GENDER MATCHING AND COMPETITIVENESS: EXPERIMENTAL EVIDENCE

This paper experimentally investigates if and how people's competitiveness depends on their own gender and on the gender of people with whom they interact. Participants are given information about the gender of the co‐participant they are matched with, they then choose between a tournament or a piece rate payment scheme, and finally perform a real task. As already observed in the literature, we find that significantly more men than women choose the tournament. The gender of the co‐participant directly influences men's choices (men compete less against other men than against women), but only when the gender information is made sufficiently salient. A higher predicted competitiveness of women induces more competition. Giving stronger tournament incentives, or allowing the participants to choose the gender of their co‐participant, increases women's willingness to compete, but does not close the gender gap in competitiveness. (JEL C70, C91, J16, J24, J31, M52)     

Inequity aversion revisited

Using a laboratory experiment, we study the predictive power of the Fehr–Schmidt (1999) model of inequity aversion and its robustness to reciprocity and stakes. We find stronger evidence for the model’s predictive power at the individual level than what the existing literature suggests. This finding is robust to stakes. However, the model’s predictive power is highly reduced if subjects can reciprocate others’ actions. This suggests that parameter estimates obtained in an environment that allows for reciprocal responses yield a bias in the parameter estimates. In particular, previous estimates (especially of the disutility of disadvantageous inequity aversion) may overestimate the importance of inequity aversion.     

Gender differences in tournament and flat-wage schemes: An experimental study

We present a new experiment that explores gender differences in both performance and compensation choices. While most of the previous studies have focused on tournament vs. piece-rate schemes, the originality of our study consists in examining the gender gap in the context of a flat wage scheme. Our data indicate that females exert a significantly higher effort than men in fixed payment schemes. We find however no gender difference in performance under the tournament scheme, due to a combination of two effects. On the one hand, men more significantly increase their effort when switching from a flat wage to a tournament scheme. On the other hand, when switching from the flat wage to a tournament scheme, women have less margin to increase performance since their effort was already relatively high with a flat wage. We also find that females are more likely than males to choose a flat-wage scheme than a tournament. This gap however narrows dramatically when feedback on previous experience is provided.     

Conditioning the effect of prize on tournament self-selection

This study examines how past performance moderates the effect of the size of the prize on tournament self-selection. We identify two types of trajectories that play simultaneous and unique roles in moderating the influence of prize on an agent’s decision to enter a tournament: within-period trajectory, which reflects an agent’s short-term performance streak in the tournaments recently entered, and across-period trajectory, which reflects an agent’s long-term performance streak in the same tournament across different periods. We find that positive (negative) within-period and across-period trajectories strengthen (weaken) the positive effect of the size of the prize on tournament entry. Although both performance trajectories have a significant and sizable influence, we find that within-period trajectory plays the strongest moderating effect. We draw on the representativeness heuristic and the availability heuristic to explain our findings. We study these notions using 54,915 self-selection decisions that professional golfers have taken over a ten-year period (1996–2006) when entering PGA Tour tournaments. We draw implications for the craft of contest design.     

Competition-induced punishment of winners and losers: Who is the target?

We elicit punishment after competition. Our experiment creates a setting in which winners and losers are assigned in a pairwise speed-based calculation task. As in Abbink and Sadrieh’s (2009) joy-of-destruction game punishment is executed by burning parts of another participant’s endowment. We manipulate the target of punishment to investigate whether it is driven by discrimination of the direct opponent, the outgroup or by joy of destruction. Furthermore, we analyze the role that the clarity of victory or defeat plays for punishment after competition. Our findings suggest that losers face punishment from particularly dominant winners and—to a lesser degree—from particularly frustrated losers. Winners face undifferentiated punishment from all sides. Our results have implications for the prevention of destructive behavior within organizations which use competitions in order to induce effort.     

Smallest tournaments not realizable by $${\frac{2}{3}}$$-majority voting

Define the predictability number α(T) of a tournament T to be the largest supermajority threshold for which T could represent the pairwise voting outcomes from some population of voter preference orders. We establish that the predictability number always exists and is rational. Only acyclic tournaments have predictability 1; the Condorcet voting paradox tournament has predictability ; Gilboa has found a tournament on 54 alternatives (i.e. vertices) that has predictability less than , and has asked whether a smaller such tournament exists. We exhibit an 8-vertex tournament that has predictability , and prove that it is the smallest tournament with predictability <  . Our methodology is to formulate the problem as a finite set of two-person zero-sum games, employ the minimax duality and linear programming basic solution theorems, and solve using rational arithmetic. D. Shepardson was supported by a NSF Graduate Research Fellowship during the course of this work.     

Observing your competitor - The role of effort information in two-stage tournaments

We consider two-stage tournaments with different information structures: Either competitors observe each others’ first-stage effort before entering the second stage or not. In laboratory experiments, we observe that subjects adjust their effort to the effort information (if available): While subjects who lead continue to exert the higher effort, they tend to lower their effort relative to the first stage, whereas those who lag increase it. Moreover, the larger the first-stage effort gap, the lower are second-stage efforts. These observations are consistent with our predictions for status-concerned subjects who care about their relative (interim) standing and the size of the effort gap.     

Advice from women and men and selection into competition

Advice processes are omnipresent in our professional and private lives. We use a laboratory experiment to study how gender and gender matching affect advice giving and how gender matching affects advice following about entry into a real-effort tournament. For advice giving we find that women are less likely than men to recommend tournament entry to advisees than are intermediate performers. Furthermore, women maximize less often the expected earnings of advisees than intermediate performers. For advice following we find that men enter the tournament significantly more often than women in the intermediate-performance group do. Gender matching does not seem to affect advice giving or following. Overall, when it is less clear what the better advice or decision is, gender differences emerge. These results are consistent with findings in other areas that document that gender differences emerge in situations that are more ambiguous.     

A smallest tournament for which the Banks set and the Copeland set are disjoint

Given a tournament T, a Banks winner of T is the first vertex of any maximal (with respect to inclusion) transitive subtournament of T; a Copeland winner of T is a vertex with a maximum out-degree. In this paper, we show that 13 is the minimum number of vertices that a tournament must have so that none of its Copeland winners is a Banks winner: for any tournament with less than 13 vertices, there is always at least one vertex which is a Copeland winner and a Banks winner simultaneously. Received: 2 May 1997 / Accepted: 30 September 1997     

A note on contestation-based tournament solutions

In tournaments, one alternative contests another if is a “winner” among only alternatives that beat it. This paper examines the consequences and limitations of the contestation relation by considering a procedure in which alternatives that are contested are iteratively eliminated from consideration. In doing so, a new family of tournament solutions are introduced and related to existing refinements of the Banks set. Findings show that iterated removal of contested alternatives a limited device for choosing from tournaments. These results contrast with results regarding the top-set of the contestation relation. Results highlight the role of the top-set operator for choice from tournaments.     

A counterexample to a conjecture of Schwartz

In 1990, motivated by applications in the social sciences, Thomas Schwartz made a conjecture about tournaments which would have had numerous attractive consequences. In particular, it implied that there is no tournament with a partition A, B of its vertex set, such that every transitive subset of A is in the out-neighbour set of some vertex in B, and vice versa. But in fact there is such a tournament, as we show in this article, and so Schwartz’ conjecture is false. Our proof is non-constructive and uses the probabilistic method.