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)     

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)     

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)     

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)     

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)     

RISK AVERSION AND OVERBIDDING IN FIRST PRICE SEALED BID AUCTIONS: NEW EXPERIMENTAL EVIDENCE

Bidding above the risk‐neutral Nash equilibrium in first price sealed bid auctions has traditionally been ascribed to risk aversion. Later studies, however, offer other explanations and even argue that risk aversion plays no or a minor role. In a novel experimental design, we directly test the relationship between risk aversion and overbidding by systematically varying the distribution of risk attitudes in auction markets. We find a significant relationship between our measure of risk aversion and overbidding. (JEL D44, C91)     

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)     

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.     

OPTIMAL PRICE OF ENTRY INTO A COMPETITION

A continuum of contestants are choosing whether to enter a competition. Each contestant has a type, and of those who enter, the ones with highest types receive prizes. A profit‐maximizing firm controls entry, and charges a price for it. I show that an increase in the value of each prize leads the firm to raise the price while keeping the intensity of entry fixed. Conversely, when the mass of prizes increases, the firm initially keeps the price constant while allowing entry to increase; and later—raises the price. (JEL C72, D82, D83)     

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)     

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)     

NETWORK STRUCTURE IN A LINK FORMATION GAME: AN EXPERIMENTAL STUDY

In this article, we use an experiment to evaluate the performance of alternative refinements in a Myersonian link formation game with a supermodular payoff function. Our results show that a non‐cooperative refinement, the global games (GG) approach, outperforms alternative cooperative refinements (strong Nash equilibrium, coalition‐proof Nash equilibrium, and pairwise stable Nash equilibrium) in explaining the observed experimental behavior in the static game of complete information with three players. The results are robust to some comparative statics and the GG approach shows a high predictive power under incomplete information. However, under repeated interaction or with a greater number of players, the GG approach loses predictive power, but so do the cooperative refinements. The results illustrate the importance of coordination failure in practice and the need to design mechanisms to reduce this effect in practical decision‐making problems. (JEL C70, C92, D20, D44, D82)     

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)     

Unclaimed Prize Information Biases Perceptions of Winning in Scratch Card Gambling

Unclaimed prize information (i.e., the number of prizes still available to be won) is information commonly provided to scratch card gamblers. However, unless the number of tickets remaining to be purchased is also provided, this information is uninformative. Despite its lack of utility in assisting gamblers in choosing the most favourable type of scratch card to play, we hypothesized that unclaimed prize information would bias participants’ judgments within a scratch card gambling context. In Experiment 1 (N?=?201), we showed that participants are influenced by this information such that they felt more likely to win, were more excited to play, and preferred to hypothetically purchase more of the scratch card with the greatest number of unclaimed prizes. In Experiment 2 (N?=?201), we attempted to ameliorate this bias by providing participants with the number of tickets remaining to be purchased and equating the payback percentages of all three games. The bias, although attenuated, still persisted in these conditions. Finally, in Experiment 3 (N?=?200), we manipulated the hypothetical scratch cards such that games with the highest number of unclaimed prizes were the least favourable, and vice versa. As in Experiment 2, participants still favoured cards with greater numbers of unclaimed prizes. Possible mechanisms underlying this bias are discussed. In conclusion, across three experiments, we demonstrate that salient unclaimed prize information is capable of exerting a strong effect over judgments related to scratch card games.     

DO RENT‐SEEKING GROUPS ANNOUNCE THEIR SHARING RULES?

We study collective rent seeking between two groups in which each group has the option of releasing or not its sharing‐rule information. First, we show that the case where both groups release their sharing‐rule information never occurs in equilibrium; when the players are unevenly matched, one group releases its sharing‐rule information and the other does not. Then, we select the Pareto‐superior equilibrium when the players are unevenly matched. We show that, in this selected equilibrium, the underdog releases its sharing‐rule information, and the favorite does not; thus, the underdog becomes the leader, and the favorite the follower (JEL D72).     

Volatility,House Edge and Prize Structure of Gambling Games

This study used simulations to examine the effect of prize structure on the outcome volatility and the number of winners of various game configurations. The two most common prize structures found in gambling games are even money payoff games (bet 1; win1; win 2) found on most table games and multilevel prizes structures found in gambling machine games. Simulations were set up to examine the effect of prize structure on the long-term outcomes of these games. Eight different prize structures were compared in terms of the number of winners and volatility. It was found that the standard table game and commercial gambling machines produced fairly high numbers of short term winners (1 h), but few long term winners (50 h). It was found that the typical even money game set up produced the lowest level of volatility. Of the multilevel prize structures examined, the three simulations based on commercial gambling machines were the least volatile. The results are examined in terms of the pragmatics of game design.     

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)     

PRIZE‐BASED MECHANISMS FOR FUND‐RAISING: THEORY AND EXPERIMENTS

We study the optimal design of mechanisms for the private provision of public goods in a setting in which donors compete for a prize of commonly known value. We discuss equilibrium bidding in mechanisms that promote both conditional cooperation and competition (i.e., the lottery and the all‐pay auction with the lowest‐bid payment rule) and rank their fund‐raising performance vis‐à‐vis their standard (pay‐your‐own‐bid) counterparts. The theoretically optimal mechanism in this model is the lowest‐price all‐pay auction—an auction in which the highest bidder wins the prize and all bidders pay the lowest bid. The highest amount for the public good is generated in the unique, symmetric, mixed‐strategy equilibrium of this auction. In the laboratory, the theoretically optimal mechanism generates the highest level of donations with three bidders but not with two bidders. (JEL D44, D64)     

THE ATTACK‐AND‐DEFENSE GROUP CONTESTS: BEST SHOT VERSUS WEAKEST LINK

This study analyzes a group contest in which one group (defenders) follows a weakest link, whereas the other group (attackers) follows a best shot impact function (IF). We fully characterize the Nash and coalition‐proof equilibria and show that with symmetric valuation the coalition‐proof equilibrium is unique up to the permutation of the identity of the active player in the attacker group. With asymmetric valuation, it is always an equilibrium for one of the highest valuation players to be active; it may also be the case that the highest valuation players in the attacker group free‐ride completely on a group member with a lower valuation. However, in any equilibrium, only one player in the attacker group is active, whereas all the players in the defender group are active and exert the same effort. We also characterize the Nash and coalition‐proof equilibria for the case in which one group follows either a best shot or a weakest link but the other group follows an additive IF. (JEL C72, D70, D72, D74, H41)     

THE MORAL COSTS OF NASTINESS

We introduce two variants of the one‐shot joy‐of‐destruction minigame (mini‐JOD). Two players are endowed with the same amount of money. They simultaneously decide whether or not to reduce the other player's payoff at an own cost. In one treatment there was a probability that nature would destroy the opponent's money anyway. We test whether this feature reduces the moral costs of nastiness, and find that destruction rates rise significantly, despite the absence of strategic reasons. (JEL C72, C91, D03)