Disappointment aversion in tournaments

Many experiments and field studies indicate that individuals have an asymmetric attitude towards gains versus losses. In this paper, we extend the canonic tournament model by assuming the workers' preferences exhibit disappointment aversion. First, we find the winning prize is first increasing and then decreasing in volatility and the losing prize shows the opposite. Furthermore, when the volatility exceeds a threshold, both the winning and losing prizes are reduced to zero. By contrast, there is no such kink for the risk aversion case. Finally, we find the piece rates always dominate rank-order tournaments when the workers are disappointment averse.     

Envy and Compassion in Tournaments

Many experiments and field studies indicate that most individuals are not purely motivated by material self-interest but also care about the well being of others. In this paper, we examine tournaments among inequity averse agents, who dislike disadvantageous inequity (envy) and advantageous inequity (compassion). It turns out that inequity averse agents exert higher efforts than purely self-interested agents for a given prize structure. Contrary to standard tournament theory, first-best efforts cannot be implemented when prizes are endogenous. Furthermore, the choice between vertical and lateral promotions is examined and it is shown that inequity costs have to be traded off against losses in human capital .     

Allocation of Prizes in Contests with Participation Constraints

We study all‐pay contests with an exogenous minimal effort constraint where a player can participate in a contest only if his effort (output) is equal to or higher than the minimal effort constraint. Contestants are privately informed about a parameter (ability) that affects their cost of effort. The designer decides about the size and number of prizes. We analyze the optimal prize allocation for the contest designer who wishes to maximize either the total effort or the highest effort. It is shown that if the minimal effort constraint is relatively high, the winner‐take‐all contest in which the contestant with the highest effort wins the entire prize sum does not maximize the expected total effort or the expected highest effort. Rather, a random contest in which the entire prize sum is equally allocated to all the participants yields a higher expected total effort as well as a higher expected highest effort.     

Contests with multiple alternative prizes: Public-good/bad prizes and externalities

We study contests in which there are multiple alternative public-good/bad prizes, and the players compete, by expending irreversible effort, over which prize to have awarded to them. Each prize may be a public good for some players and a public bad for the others, and the players expend their effort simultaneously and independently. We first prove the existence of a pure-strategy Nash equilibrium of the game, then establish when the total effort level expended for each prize is unique across the Nash equilibria, and then summarize and highlight other interesting and important properties of the equilibria. Finally, we discuss the effects of heterogeneity of valuations on the players’ equilibrium effort levels and a possible extension of the model.     

Principal‐agent and Peer Relationships in Tournaments

Effort provision in tournaments may depend on both social preferences towards the competitor and social preferences towards the principal who designed the tournament. In a laboratory experiment, we analyze agents' behavior in different tournament settings that vary the distribution of the prize between agents. The principal chooses between a low and a high guaranteed payment. Standard economic theory predicts the same effort provision in all situations. Instead, our results show that both the generosity of the principal and the strict separation between winner and loser increase the effort level in tournaments. Moreover, agents focus their preferences either on the principal or on the agent. Copyright © 2014 John Wiley & Sons, Ltd.     

Endogenous versus exogenous allocation of prizes in teams—Theory and experimental evidence

We present a model where compensation within a team is determined either exogenously by a third party or endogenously through a bargaining process among team members. In the exogenous case, we compare equal rewards with a tournament design. In the endogenous case, members compete in their efforts for the right to propose the distribution of the prize. Failure to reach an agreement on the proposal is costly and the role of proposer rotates in the order of members' efforts. We show in an experiment that tournaments induce higher efforts than equal rewards and that the influence of exogenously or endogenously allocating the prize depends on the specific bargaining rules in the endogenous case.     

Your failure is my opportunity—Effects of elimination in contests

In this paper, we consider a sequence of multi-prize all-pay auctions, where low-performing players are eliminated along the way. We provide sufficient conditions such that equilibrium behavior is unaffected by the prospects of winning prizes in later rounds. When these conditions are not met, we identify a novel externality effect and derive equilibria in a model with two rounds. We compare our results to knockout tournaments in which players are partitioned into subcontests in each round.     

Preemptive behavior in sequential-move tournaments with heterogeneous agents

Rank-order tournaments are usually modeled simultaneously. However, real tournaments are often sequential. We show that agents' strategic behavior in sequential-move tournaments significantly differ from the one in simultaneous-move tournaments: In a sequential-move tournament with heterogeneous agents, the first acting agent may choose a preemptively high effort so that the following agent gives up. The principal is able to prevent preemptive behavior in equilibrium by choosing a sufficiently small spread between winner and loser prize. Received: January 2003, Accepted: November 2004 JEL Classification: J3, M12, M5 We would like to thank two anonymous referees and the editor Kai Konrad for helpful comments. Financial support by the Deutsche Forschungsgemeinschaft (DFG), projects no. KR 2077/2-1 and SFB/TR 15 ("Governance and the Efficiency of Economic Systems"), is gratefully acknowledged.     

MULTIPLE-PRIZE CONTESTS – THE OPTIMAL ALLOCATION OF PRIZES

Abstract.  Multiple-prize contests are important in various fields of economics ranging from rent seeking over labour economics, patent and R&D races to tendering for (governmental) projects. Hence it is crucial to understand the incentive effects of multiple prizes on effort investment. This survey attempts to outline, compare and evaluate the results from the literature. While a first prize always results in a positive incentive to invest effort, second and later prizes lead to ambiguous effects. Depending on the objective function, the characteristics of the individuals and the type of contest a different prize allocation is optimal.     

Relative deprivation in rank-order tournaments

This paper examines the influence of relative deprivation (RD), based on net income, on the strategy choice of workers in tournaments. The results show that for given tournament prizes, workers who experience RD exert more effort than workers who maximize their expected absolute incomes. These findings hold for productive effort as well as for counterproductive effort (sabotage). In addition, the paper discusses various implications that arise when the employer can choose between different compensation schemes in the tournament.     

Copycat gaming: A spatial analysis of state lottery structure

In models of tax competition, tax instruments are explicit; all parties are aware of the tax and respond to incentives provided therein. In the case of state lotteries, the tax is the amount of sales collected but not redistributed as prizes. Using data from 1967 to 2000, we show that although such a tax is implicit, states still engage in tax competition; if neighboring states raise their prize payout by 10% (thereby lowering their lottery tax), the home state will respond with up to a 5% increase in their prize payout.     

Optimal lottery

This article proposes an equilibrium approach to lottery markets in which a firm designs an optimal lottery to rank-dependent expected utility (RDU) consumers. We show that a finite number of prizes cannot be optimal, unless implausible utility and probability weighting functions are assumed. We then investigate the conditions under which a probability density function can be optimal. With standard RDU preferences, this implies a discrete probability on the ticket price, and a continuous probability on prizes afterwards. Under some preferences consistent with experimental literature, the optimal lottery follows a power-law distribution, with a plausibly extremely high degree of prize skewness.     

Human Capital Spillovers within the Workplace: Evidence for Great Britain*

In this paper, we use a unique matched worker–workplace data set to estimate the effect on own earnings of co‐workers’ education. Our results, using the 1998 GB Workplace Employee Relations Survey, show significant effects. An independent, significantly positive effect from average workplace education is evident; own earnings premia from years of education fall only slightly when controlling for workplace education. This result suggests that the social returns to education are strongly positive – working with colleagues who each had 1.2 years (1 standard deviation) of more education than the average worker, boosts own earnings by 11.1%. An additional year of any single co‐worker's education is worth about 3.2% of an additional own year of education. We also test for interactions between own and co‐worker education levels and for ‘skills incompatibility’ when worker education levels are heterogeneous. The interactions appear negative: own education is not much valued at workplaces where co‐workers’ education levels are already high. There is no evidence that workplace heterogeneity in worker education levels adversely affects own earnings. This result runs counter to theoretical predictions, and suggests that workers compete in tournaments for high‐paying jobs.     

Credibility and Monitoring: Outsourcing as a Commitment Device

We analyze an environment plagued by double moral hazard where the agent’s effort level and the principal’s precision in monitoring are not contractible. In such an environment, the principal tends to over‐monitor thereby inducing low effort. To ease the latter problem, the principal may choose to increase monitoring costs by outsourcing the activity. As a result equilibrium monitoring is reduced and incentives become more powerful. This choice is particularly likely when the worker’s effort is an important factor in determining output.     

Time Discounting in Strategic Contests

In many contests, such as political campaigns or R&D expenditures, there is at least some trade‐off between immediate money outlay and potential future benefits. This timing aspect has mostly been ignored by the contest literature. If contestants exhibit a strong present bias, such as that shown by past individual choice experiments, then benefits that are deferred to the future will lead to a significant drop in investment. This paper uses controlled laboratory experiments to explore how the timing of prize payment impacts behavior in a contest with a unique Nash equilibrium strategy. We find no evidence that people significantly discount future prizes in our contests, despite the fact that we do replicate present bias in a separate individual choice experiment.     

On sabotage in collective tournaments

In this paper a tournament between teams (a collective tournament) is considered, where each contestant may spend productive effort in order to increase his team’s performance or sabotage the members of the opponent team. It is shown that each team directs all its sabotage activities at exactly one of the opponent team’s least able members. This is due to two effects, a decreasing-returns effect and a complementarity effect. The result is of particular interest, as findings on individual tournaments indicate that very able players should usually be sabotaged most strongly.     

Optimal Hedging Strategies and Interactions between Firms

This paper studies corporate risk management in a context of financial constraints and imperfect competition in the product market. The paper shows that interactions between firms affect their hedging strategies. As a general rule, firms’ hedging demands decrease with the correlation between their internal funds and investment opportunities. Moreover, when a firm’s hedging demand is high in the case where investments are strategic substitutes, its hedging demand is low in the case where investments are strategic complements and vice versa.     

Contingent payments in selection contests

The early literature on research contests stressed the advantages of a fixed prize in inspiring R&D effort. More recently the focus has moved towards endogenizing the rewards to research activity in these tournament settings, since this can induce extra effort or enhance the surplus of the buyer. We focus on a research contest as a means of selecting a partner for an R&D enterprise, in an informational setting in which the established providers of R&D services know more about each others’ relative capabilities than does the buyer/sponsor. An alternative use of our model is in choosing between prospective patentees where the Patent Trading Office has less information on the patents than the competitors. This asymmetry creates a source of inefficiency if a rank order contest is used as a selection device; we show how the contest can be modified to improve selection efficiency, while maintaining its simplicity (as only ordinal information is required). The modification that we suggest involves endogenizing the prizes that are awarded contingent upon whether a contestant wins or loses the contest. Furthermore, the payment system and the selection mechanism are detail-free. This paper is part of the project “The Knowledge-Based Society” sponsored by the Research Council of Norway (project 172603/V10).     

The O‐ring theory of the firm

We develop an O‐ring production function characterized by specialization and division of labor and where shirking or negative shocks can have major adverse consequences. We show that when the principal can monitor individual output, the firm tends be large (potentially larger than first best), with a high degree of specialization and division of labor, weak incentives, and low pay as in traditional nonunion manufacturing. Moral hazard can only limit the size of the firm relative to the first best when the principal can only monitor team output, in which case the firm has the opposite characteristics.     

Winner’s effort maximization in large contests

We investigate the temporal structure that maximizes the winner’s effort in large homogeneous contests. We find that the winner’s effort ranges from a lower bound of 0 to an upper bound of one third of the value of the prize, depending on the temporal structure; the upper (lower) bound is approached with an infinite number of players playing sequentially (simultaneously) in the first periods (period). Nevertheless, when the number of players is large but finite, we show that winner’s effort is maximized when all players play sequentially except in the very last period and that, within the family of such optimal temporal structures, more players play simultaneously in the very last period than sequentially in all other periods. Furthermore, out of all players, the percentage of those playing simultaneously in the very last period goes to 100% as the number of players grows larger and larger.