CONTESTS WITH DRAWS: AXIOMATIZATION AND EQUILIBRIUM

We introduce and axiomatize a class of single‐winner contest success functions that embody the possibility of a draw. We then analyze the game of contest that our success functions induce, having different prizes delivered in the occurrence of a win and a draw. We identify conditions for the existence and uniqueness of a symmetric interior Nash equilibrium and show that equilibrium efforts and equilibrium rent dissipation can be larger than in a Tullock contest (with no possibility of a draw) due to increased competition even if the draw‐prize is null. These results suggest that a contest designer may profit from introducing the possibility of a draw. Finally, we show that this approach naturally extends to multiprize contests with multiple draws across different subsets of the set of players. (JEL C72, D72, D74)     

CONTEST DESIGN: AN EXPERIMENTAL INVESTIGATION

This paper experimentally compares the performance of four simultaneous lottery contests: a grand contest, two multiple prize settings (equal and unequal prizes), and a contest which consists of two subcontests. Consistent with the theory, the grand contest generates the highest effort levels among all simultaneous contests. In multi‐prize settings, equal prizes produce lower efforts than unequal prizes. The results also support the argument that joint contests generate higher efforts than an equivalent number of subcontests. Contrary to the theory, there is significant over‐dissipation. This over‐dissipation can be partially explained by strong endowment size effects. Subjects who receive higher endowments tend to over‐dissipate, whereas such over‐dissipation disappears when the endowments are lower. This behavior is consistent with the predictions of a quantal response equilibrium. We also find that less risk‐averse subjects over‐dissipate more. (JEL C72, C91, D72)     

THREAT AND PUNISHMENT IN PUBLIC GOOD EXPERIMENTS

Experimental studies of social dilemmas have shown that while the existence of a sanctioning institution improves cooperation within groups, it also has a detrimental impact on group earnings in the short run. Could the introduction of pre‐play threats to punish have enough of a beneficial impact on cooperation, while not incurring the cost associated with actual punishment, so that they increase overall welfare? We report an experiment in which players can issue non‐binding threats to punish others based on their contribution levels to a public good. After observing others' actual contributions, they choose their actual punishment level. We find that threats increase the level of contributions significantly. Efficiency is improved, but only in the latter periods. However, the possibility of sanctioning differences between threatened and actual punishment leads to lower threats, cooperation, and welfare, restoring them to levels equal to or below the levels attained in the absence of threats. (JEL C92, H41, D63)     

CAPS IN SEQUENTIAL CONTESTS

We study a sequential two‐stage all‐pay auction with two identical prizes. In each stage, the players compete for one prize and each player can win either one or two prizes. The designer may impose a cap on the players' bids in each of the stages. We analyze the equilibrium in this sequential all‐pay auction with bid caps and show that capping the players' bids is profitable for a designer who wishes to maximize the players' expected total bid. (JEL D44, D82, J31, J41)     

SOCIAL HIERARCHIES: A LABORATORY STUDY ON PUNISHMENT PATTERNS ACROSS NETWORKS

We experimentally study punishment patterns across network structures, and their effect on cooperation. In a repeated public goods setting, subjects can only observe and punish their neighbors. Centralized structures (like the star network) outperform other incomplete networks and reach contribution levels like the ones observed in a complete network. Our results suggest that hierarchical network structures with a commonly observed player benefit more from sanctions not because central players punish more, but because they follow, and promote, different punishment patterns. While quasi-central players in other incomplete architectures (like the line network) retaliate, and get trapped in the vicious circle of antisocial punishment, central players in the star network do not punish back, increase their contributions when sanctioned by peripheral players, and sanction other participants in a prosocial manner. Our results illustrate recent field studies on the evolutionary prevalence of hierarchical networks. We document a network-based rationale for this positive effect in an identity-free, fully anonymous environment. (JEL C72, C91, C92, D90, H41)     

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)     

PROPERTY RIGHTS AND LOSS AVERSION IN CONTESTS

We analyze the effects of property rights and the resulting loss aversion on contest outcomes. We study three situations: in “gain” two players start with no prize and make sunk bids to win a prize; in “loss” both the players start with prizes and whoever loses the contest loses their prize; and in “mixed” only one player starts with a prize that stays with him if he wins, but is transferred to the rival otherwise. Since the differences among the treatments arise only from framing, the expected utility and the standard loss aversion models predict no difference in bids across treatments. We introduce a loss aversion model in which the property rights are made salient, and as a result the reference point varies across treatments. This model predicts average bids in descending order in the loss, the mixed, and the gain treatment; and higher bids by the player with property rights in the mixed treatment. The results from a laboratory experiment broadly support these predictions. There is no significant difference in bids in the loss (gain) treatment and bids by property rights holder (nonholder) in the mixed treatment. A model incorporating both loss aversion and social preferences explains this result. (JEL C91, C72, D23, D74)     

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)     

ON THE PREFERENCES OF PRINCIPALS AND AGENTS

One of the reasons why market economies are able to thrive is that they exploit the willingness of entrepreneurs to take risks that laborers might prefer to avoid. Markets work because they remunerate good judgment and punish mistakes. Indeed, modern contract theory is based on the assumption that principals are less risk averse than agents. We investigate if the risk preferences of entrepreneurs are different from those of laborers by implementing experiments with a random sample of the population in a fast‐growing, small‐manufacturing, economic cluster. As assumed by theory, we find that entrepreneurs are more likely to take risks than hired managers. These results are robust to the inclusion of a series of controls. This lends support to the idea that risk preferences is an important determinant of selection into occupations. Finally, our lotteries are good predictors of financial decisions, thus giving support to the external validity of our risk measures and experimental methods (JEL C93, D81, D86).     

LINKING WEALTH AND PUNISHMENT EFFECTIVENESS: PUNISHMENT AND COOPERATION UNDER CONGRUENT HETEROGENEITIES

Global and local cooperation in supplying global public goods is often insufficient. In this respect, laboratory experiments show that peer punishment is an effective cooperation-enhancing instrument. However, it is unclear whether peer punishment would facilitate cooperation and public good provision even under congruent heterogeneities in wealth and punishment effectiveness. To this end, we experimentally study the effect of peer punishment under joint heterogeneities, where either the richest or the poorest member is also the most effective punisher. We compare these joint heterogeneities to treatments with single heterogeneities in either endowment or punishment effectiveness and to a baseline symmetry treatment with homogeneous parties. We find that heterogeneity in punishment effectiveness does not matter for cooperation, whereas endowment heterogeneity reduces cooperation compared to symmetry. This is because rich members contribute a lower portion of their endowment to the public good than their poorer counterparts. We also observe that cooperation is higher under joint heterogeneities in endowment and punishment effectiveness than under endowment heterogeneity (with no differences than under symmetry). This holds even when the rich party gains less from cooperation and is the most effective punisher. (JEL C92, D74, H41)     

Sequential contests with synergy and budget constraints

We study a sequential Tullock contest with two stages and two identical prizes. The players compete for one prize in each stage and each player may win either one or two prizes. The players have either decreasing or increasing marginal values for the prizes, which are commonly known, and there is a constraint on the total effort that each player can exert in both stages. We analyze the players’ allocations of efforts along both stages when the budget constraints (effort constraints) are either restrictive, nonrestrictive or partially restrictive. In particular, we show that when the players are either symmetric or asymmetric and the budget constraints are restrictive, independent of the players’ values for the prizes, each player allocates his effort equally along both stages of the contest.     

CITATIONS AND INCENTIVES IN ACADEMIC CONTESTS

I consider a contest between scholars on the basis of three popular indices of citation. There exist equilibria in which there are more and better-quality papers in the total citations contest than in the h-index contest. In some cases, the total citations contest yields the same quality of papers but more papers than the Euclidean contest. As the cost of writing a paper increases,the h-index is inferior to the total citations index in both the quality and quantity of papers. This result is partly driven by how the number of papers constrains how the h-index counts citations. (JEL D72)     

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)     

SIMULTANEOUS DECISION‐MAKING IN COMPETITIVE AND COOPERATIVE ENVIRONMENTS

We experimentally investigate simultaneous decision‐making in two contrasting environments: one that encourages competition (lottery contest) and one that encourages cooperation (public good game). We find that simultaneous participation in the public good game affects behavior in the contest, decreasing sub‐optimal overbidding. Contributions to the public good are not affected by participation in the contest. The direction of behavioral spillover is explained by differences in strategic uncertainty and path‐dependence across games. Our design allows us to compare preferences for cooperation and competition. We find that in early periods, there is a negative correlation between decisions in competitive and in cooperative environments. (JEL C72, C91)     

GUILTY CONSCIENCE AND INCENTIVES WITH PERFORMANCE ASSESSMENT ERRORS

This study examines the effects of guilty conscience on incentive in the situation where an agent performance assessment has errors. There are two types of assessment error: undervaluation and overvaluation. In overvaluation, agents will not correct the assessment because their wages would then decrease. Although agents will want their undervaluation corrected, principals will not correct the error due to increased wage cost. Hence, correcting errors is complicated. However, this type of selfish behavior by agents and principals produces feelings of guilt, particularly when others trust them. In this situation, a high incentive is desirable for conscientious people with a strong sense of guilt or for nonconscientious people who do not feel guilt, but it is undesirable for intermediate‐type people who are conscientious only to a certain extent. (JEL D03, D82, J41)     

EXCLUSION AND REINTEGRATION IN A SOCIAL DILEMMA

Using a social dilemma game, we study the cooperative behavior of individuals who reintegrate their group after being excluded by their peers. We manipulate the length of exclusion and whether this length is imposed exogenously or results from a vote. We show that people are willing to exclude the least cooperators and they punish more, and more severely, chronic defections. In return, a longer exclusion has a higher disciplining effect on cooperation after reintegration, but only when the length of exclusion is not chosen by group members. Its relative disciplining effect on cooperation after reintegration is smaller when the length of exclusion results from a vote. In this environment, a quicker reintegration also limits retaliation. The difference in the impact of long versus short exclusion on retaliation is larger when the length of exclusion is chosen by group members than when it is exogenous. Post-reintegration cooperation and forgiveness depend not only on the length of exclusion but also on the perceived intentions of others when they punish. (JEL C92, H41, D23)     

PROCEDURAL UNFAIR WAGE DIFFERENTIALS AND THEIR EFFECTS ON UNETHICAL BEHAVIOR

In this paper, we investigate how payment procedures that are deemed unfair can spur unethical behavior towards innocent coworkers in a real-effort experiment. In our Discrimination treatment, a highly unfair payment procedure with wage differentials, half the workforce is randomly selected and paid by relative performance whereas the remaining receives no payment. A joy-of-destruction game measures unethical behavior subsequently. Non-earners in Discrimination destroy significantly more than in the non-discriminatory control treatments. In Discrimination, unethical behavior is generally high for all non-earners, independent of individual inequality aversion and relative performance beliefs. In the control treatments, inequality aversion is the main driver of destructive behavior. (JEL C91, D03, J33, J70, M52)     

VOTING, PUNISHMENT, AND PUBLIC GOODS

Researchers have found that voting can help increase voluntary contributions to a public good—provided enforcement through a third party. Not all collective agreements, however, guarantee third-party enforcement. We design an experiment to explore whether a voting rule with and without endogenous punishment increases contributions to a public good. Our results suggest that voting by itself does not increase cooperation, but if voters can punish violators, contributions increase significantly. While costly punishment increases contributions at the price of lower efficiency, overall efficiency for a voting-with-punishment rule still exceeds the level observed for a voting-without-punishment rule. ( JEL C92, D72, H41)     

Punishment and status in collective action: How status hierarchies foster optimal punishment use

I provide a brief overview of the literature on human cooperation, punishment, and social dilemmas. After reviewing relevant literature, I move on to a series of predictions, intertwining findings on punishment, public goods, and social status. Leaning on Status Characteristics Theory, I explicate how the behavioral expectations that we derive from status positions foster a means of using punishment to secure public goods. Furthermore, I argue that we carry general expectations for high status actors to punish when deemed collectively necessary. Building on this expectation, I articulate how initially status‐homogenous groups can develop status ranks on the basis of punishment behavior, allowing task groups to mimic sanctioning institutions commonly seen in public goods research and everyday life.     

THE PERFORMANCE EFFECTS OF WISE AND UNWISE MANAGERIAL DISMISSALS

The decision to dismiss a coach is challenging because poor performance tends to coincide with both bad luck and low coaching ability. We differentiate between dismissals following actual poor performance on the pitch (wise dismissals) and dismissals following seemingly poor performance due to bad luck (unwise dismissals). To categorize dismissals, we use “expected goals,” which are less vulnerable to random variation in match outcomes. Using data from European football, we find that wise dismissals increase subsequent performance compared to a control group of nondismissals with similarly poor performance on the pitch. However, unwise dismissals do not improve subsequent performance compared to a control group with similar strings of bad luck. (JEL D81, J44, L83)