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)     

WHY ZERO TOLERANCE OF MISCONDUCT IS UNDESIRABLE IN CONTESTS

Competition can foster misconduct in any circumstance where the organizer of a contest cannot perfectly monitor contestants' actions or when doing so is prohibitively costly. Although misconduct comprises all actions that are contrary to the interest of the organizer, it is not necessarily the case that it is optimal to prohibit all such behavior. In this paper, we determine the equilibrium level of misconduct chosen by players in a symmetric rank‐order tournament between two competitors in which the organizer tolerates some level of misconduct. In addition to showing that zero tolerance may not minimize the level of misconduct in equilibrium, we show that there exists a range of tolerated misconduct where a symmetric mixed strategy equilibrium exists with players cheating (i.e., misconduct above the tolerated level) with some probability. When the gain from misconduct is uncertain and unknown the contest organizer faces a tradeoff: tolerating more misconduct will reduce such behavior when the state of temptation is high, but increase it when temptation is low. (JEL J33, K42)     

SELECTIVE RECOGNITION: HOW TO RECOGNIZE DONORS TO INCREASE CHARITABLE GIVING

Recognizing donors by revealing their identities is important for increasing charitable giving. Using a framed field experiment, we show that all forms of recognition that we examine increase donations relative to the baseline treatment, and recognizing only the highest or only the lowest donors has the strongest and significant effect. We argue that selective recognition creates tournament‐like incentives. Recognizing the highest donors activates the desire to seek a “positive prize” of prestige, while recognizing the lowest donors activates the desire to avoid a “negative prize” of shame. We discuss how selective recognition can be used by charities to increase donations. (JEL C93, D64)     

The replacement principle in economies with indivisible goods

 We consider the problem of allocating a list of indivisible goods and some amount of an infinitely divisible good among agents with equal rights on these resources, and investigate the implications of the following requirement on allocation rules: when the preferences of some of the agents change, all agents whose preferences are fixed should (weakly) gain, or they should all (weakly) lose. This condition is an application of a general principle of solidarity discussed in Thomson (1990b) under the name “replacement principle”. We look for selections from the no-envy solution satisfying this property. We show that in the general case, when the number of objects is arbitrary, there is no such selection. However, in the one-object case (a single prize), up to Pareto-indifference, there is only one selection from the no-envy solution satisfying the property. Such a solution always selects an envy-free allocation at which the winner of the prize is indifferent between his bundle and the losers’ common bundle. Received: 15 May 1995 / Accepted: 5 June 1996     

ON EQUILIBRIUM PLAYER ORDERING IN DYNAMIC TEAM CONTESTS

We study equilibrium player ordering in a dynamic all-pay contest between two teams. The contest lasts two periods, and each team consists of two players who perform in different periods on behalf of their teams. The team with the higher aggregate output wins the prize, which is a public good to its players. Each team has one stronger player and one weaker player, and the two teams can differ in their values of the prize. The teams maximize their winning odds by strategically assigning their players to different periods. We find that when the intrateam heterogeneity in player ability is not excessive, the teams would allocate their stronger players to the late positions as the “anchormen.” When both the intrateam ability gap and interteam heterogeneity in teams' values become excessively large, the team with high value always places its stronger player in the early position, who will place a large bid to preempt late competition. (JEL C7, D7, D8)     

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)     

CARROTS AND STICKS: PRIZES AND PUNISHMENTS IN CONTESTS

We study optimal contest design in situations where the designer can reward high performance agents with positive prizes and punish low performance agents with negative prizes. We link the optimal prize structure to the curvature of distribution of abilities in the population. In particular, we identify conditions under which, even if punishment is costly, punishing the bottom is more effective than rewarding the top in eliciting effort input. If punishment is costless, we study the optimal number of punishments in the contest. (JEL D44, D82, J31, J41)     

PRIZE SCARCITY AND OVERDISSIPATION IN ALL‐PAY AUCTIONS

We compare bidding behavior in complete information all‐pay auction experiments that vary in the prizes and number of players. We confirm the observation from prior single‐prize experiments that there is overbidding relative to equilibrium predictions. Our primary results are that increasing the number of prizes and players proportionally does not reduce overbidding but increasing the number of prizes with a fixed number of players eliminates overbidding. We conclude that the overbidding phenomenon is related to the scarcity of the prize. We provide new theoretical results on the multi‐prize logit equilibrium, and our experimental results are qualitatively consistent with logit equilibrium predictions. (JEL D72, D91, C91, D44)     

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)     

Korea/Japan or Japan/Korea? The Saga of Co‐hosting the 2002 Soccer World Cup

Since Japan's defeat and enforced withdrawal from Korea in 1945, continuing acrimony from those 35 years of Japan's unwelcome domination on the Korean Peninsula has been a thorny issue affecting full normalization of relations between the two countries. The first round of post‐war talks between Japan and South Korea remained stalled for almost half a decade, and not until 1965, after 14 years of subsequent – and painfully drawn out – negotiations were diplomatic relations finally established. Today, in spite of a gradual thawing of that very icy relationship, Korean people's bitterness over Japan's militarist past and over what they regard as insufficient apologies and reparations was always going to feature as the two nations went head to head in their bid to host the 2002 World Cup. Following FIFA's decision in 1996 that Japan and South Korea would jointly stage the cup as co‐hosts – the first time in soccer World Cup history – extant animosity became increasingly problematic as South Korea, Japan and FIFA hammered out the details. In this paper I draw upon media coverage from the mid‐1990s to the present day to discuss FIFA's historic co‐hosting decision, a judgment which, in spite of the difficulties then and now, does have the potential to make a very positive impact on both countries and greater Asia. After briefly introducing the broader sports/politics conundrum, I outline the final stages of the host‐nation selection dilemma which forced FIFA into its unprecedented joint decision, locating that process within a framework of the competitive lobbying between the two political rivals and internal demands for a change of management style within FIFA itself. I will also highlight the economic, political, historical and social ramifications of a co‐hosted soccer World Cup and attempts to deal with the issues. South Korea's desire for North Korea to participate in the tournament will also be discussed as a vehicle for encouraging stability on the Korean Peninsula and for future cooperation between Japan and South Korea on their policies towards North Korea. Although the 2002 World Cup arrangements are already firmly in place, the long‐term animosity and the continuing accusations and points‐scoring between the two host‐nations suggest that we can not yet take it for granted that the co‐hosted 2002 soccer spectacular will go according to plan.     

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.

MARCH MADNESS? UNDERREACTION TO HOT AND COLD HANDS IN NCAA BASKETBALL

The hot hand bias is the widely documented bias toward overestimation of positive serial correlation in sequential events. We test for the hot hand bias in a novel real‐world context, the seeding of National Collegiate Athletic Association (NCAA) basketball tournament teams. That is, we examine whether teams that perform relatively well heading into “March Madness” are seeded too high, and/or teams with poor recent performance are seeded too low. The seeds are determined by a 10‐member committee that only has implicit incentives, but these incentives are still substantial as the committee's decisions are highly scrutinized by the media, fans, and other stakeholders. We find that, contra the hot hand bias, the committee underreacts to signals of momentum heading into the NCAA tournament. Various results indicate this behavior can be attributed to both: (1) inattention to relatively detailed information indicating momentum; and (2) under‐appreciation of the predictive value of this information. Betting markets incorporate this information efficiently, but neglect some additional information that is predictive of winning NCAA tournament games but not of beating the spread. We note that the NCAA tournament has been highly popular and lucrative partly due to the “madness” (high frequency of wins by lower‐seeded teams), which the bias we document contributes to, making the persistence of bias less surprising. (JEL D83, L83)     

Banks winners in tournaments are difficult to recognize

Given a tournament T, a Banks winner of T is the top vertex of any maximal (with respect to inclusion) transitive subtournament of T. In this technical note, we show that the problem of deciding whether some fixed vertex v is a Banks winner for T is NP-complete. Received: 22 February 2002/Accepted: 20 June 2002 Supported by the START program Y43-MAT of the Austrian Ministry of Science. I would like to thank two thank the referees for a careful reading of the paper, for helpful remarks, and for many suggestions how to improve the presentation.     

Gendered Congregations,Gendered Service: The Impact of Clergy Gender on Congregational Social Service Participation

Using data from the 1998 National Congregations Study, I present empirical evidence that shows that the gender of a congregation's leadership makes a difference in the likelihood that a congregation will participate in a social service programme. The results from binary logistic regression indicate that the odds of congregations with women head clergy participating in a social service programme are four times greater than those with men head clergy. In addition, as the percentage of women on a congregation's governing board increases the probability that a congregation will participate in a service project also increases. The specific types of social service programmes a congregation pursues also differ by gender of leadership, with women‐led congregations significantly more likely to pursue service projects that could be labelled feminine while avoiding programmes that are clearly feminist. To explain this gendered behaviour I incorporate Acker's (1990 ) theory of gendered organizations.     

INFORMATION AND ENDOGENOUS DELEGATION IN A RENT‐SEEKING CONTEST

We offer a new explanation for the occurrence of delegation in rent‐seeking contests. We consider a two‐player contest for a prize of common value. The players only know that the prize is high or low, with given probabilities. Each player can hire a delegate to act on his behalf. After a delegate is hired, she privately observes the true value of the prize. We derive the conditions under which, respectively, no player, only one player, or both players delegate in equilibrium. (JEL D7)     

The effect of limited search ability on the quality of competitive rent-seeking clubs

A competitive rent-seeking club (CRSC) offers its members the chance of winning a prize (status, position, privilege) by being selected, typically, by a civil servant or a politician. The selector replaces in our setting the usual contest success function; instead of determining the winner on the basis of the club-members’ efforts, he selects the winner on the basis of quality. This article focuses on the effect of incomplete search of the selector on the efficiency of democratic self-governing and decentralized RSC’s that control admittance to the club and its transparency, assuming that quality of their members is fixed. The incomplete search of the selector is assumed to take the simple form of fixed random sampling of the contestants—the members of the CRSC. Our results imply that, even when active rent-seeking expenditures are disregarded, the decisions of CRSC’s regarding their composition and transparency tend to reduce quality and are therefore inefficient.     

Uncertainty and the Rise of the Work‐Family Dilemma

Existing research argues that women's wages, consumerism, and changing attitudes dismantled the male bread‐winner system. Families' economic need is dismissed with the suggestion that mothers' rhetoric of “need” was a smoke screen to defend against social stigma for working mothers. Drawing on biennial data from 1965 to 1987, I suggest that consumptive certainty of the 1950s and 1960s gave way to economic uncertainty in the 1970s and beyond. Economic uncertainty provided impetus, legitimacy, and justification for young families to adopt new work‐family arrangements. Hence, economic uncertainty is conceptualized as a real circumstance that substantiates families' reasonable perceptions of need.     

What's in a Name When It Isn't a Word? 17‐Month‐Olds' Mapping of Nonverbal Symbols to Object Categories

Infants begin acquiring object labels as early as 12 months of age. Recent research has indicated that the ability to acquire object names extends beyond verbal labels to other symbolic forms, such as gestures. This experiment examines the latitude of infants' early naming abilities. We tested 17‐month‐olds' ability to map gestures, nonverbal sounds, and pictograms to object categories using a forced‐choice triad task. Results indicated that infants accept a wide range of symbolic forms as object names when they are embedded in familiar referential naming routines. These data suggest that infants may initially have no priority for words over other symbolic forms as object names, although the relative status of words appears to change with development. The implications of these findings for the development of criteria for determining whether a symbol constitutes an object name early in development are considered.     

Abjection and self‐identity: towards a revised account of purity and impurity

Kristeva describes abjection as ‘the repugnance, the retching that thrusts me to the side and turns me away from defilement, sewage, and muck’. Her account of the ‘abject’ has received a great deal of attention since the 1980s, in part due to high demand for theoretical attention to themes of purity and impurity, which remain important in contemporary society. Yet Kristeva herself has noted that ‘my investigation into abjection, violence and horror … picks up on a certain vacuum’, and other scholars have agreed that there is need for further work on what Campkin has described as an ‘under theorized’ topic. This article will begin by exploring the central line of criticism that has been made of Kristeva's concept of abjection, before then considering an attempt by Goodnow to address these concerns through a re‐reading of Kristeva. Goodnow's re‐reading of Kristeva, together with some conceptual clarifications from Hegel, will point the way towards a more precise account of purity and impurity. I shall contend that Kristeva's work on social abjection sometimes hits upon a pattern, which greater conceptual precision will be able to revise into a new social theory of when and why themes of purity and impurity are invoked in Western societies. It will be argued that impure phenomena are those in which heterogeneity is seen to disturb a qualitative homogeneity, taken to be basic; pure phenomena are those understood to be all‐of‐a‐piece and as a result identical with their essence.     

Prize Level and Debt Size: Impact on Gambling Behaviour

No studies to date have specifically determined the relationship between prize levels, debt size, and impulsivity on reported gambling behaviour on Electronic Gaming Machines (EGM). The present study reports the findings of a pilot study designed to investigate whether or not the likelihood of increasing the size of a bet was related to the level of prize offered and personal debt. The sample consisted of 171 first year psychology students (61 males and 120 females). Participants completed a series of gambling vignettes designed to elicit data on reported bet size according to different prize levels and debt sizes; the Eysenck Impulsivity Scale (Eysenck and Eysenck 1977); the Canadian Problem Gambling Index; and an author-constructed questionnaire eliciting data on demographic and gambling behaviours. Results indicated that as prize levels increase the odds (relative risk) of an individual placing a bet on an EGM and the amount of money reportedly bet tends to increase. A negative relationship between debt size and reported gambling behaviour moderated by prize level was found. No differences were found in the odds of placing a bet according to impulsivity. It was concluded that prize and debt sizes do influence propensities to gamble and level of bets. The findings have implications for restricting jackpot and general prize levels as a responsible gambling strategy designed to reduce motivations to gamble.