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)     

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)     

CHAOTIC DYNAMICS IN CONTESTS

Under a myopic best‐reply dynamic, efforts in repeated contests may exhibit chaotic behavior. This may help explain, for example, why experimental data often show nonconvergence to one‐shot equilibrium efforts. (JEL C61, C72, D72, D74, D83)     

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)     

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 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)     

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).     

PRIMING THE CHARITABLE PUMP: AN EXPERIMENTAL INVESTIGATION OF TWO‐STAGE RAFFLES

We experimentally study two‐stage self‐financing raffles in which participants can buy tickets in two stages. In all raffles, one half of the proceeds are donated to a local charity and the raffle winner wins the other half. The mechanisms differ by what happens to the tickets purchased in the first stage. In the complete draw down two‐stage raffle, the first stage tickets are eliminated from the active pool of tickets, while in the no draw down raffle they remain in the active pool. We find that both two‐stage raffles initially perform better than the standard one‐stage 50–50 raffle. Over time, the aggregate contribution level in the complete draw down raffle declines and approaches that of the one‐stage raffle, while in the no draw down raffle contributions are stable and remain higher than those in the other two mechanisms. In both two‐stage raffles, we observe a positive correlation between the proceeds of the first stage and the number of tickets bought in the second stage. Our results are at odds with a standard warm glow model of giving, and also cannot be explained by the joy of winning or learning about bidders' types. (JEL C72, C92, D64)     

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)     

Two-Player Asymmetric Contests with Ratio-Form Contest Success Functions

I examine players' equilibrium effort levels in two-player asymmetric contests with ratio-form contest success functions. I first characterize the Nash equilibrium of the simultaneous-move game. I show that the equilibrium effort ratio is equal to the valuation ratio, and that the prize dissipation ratios for the players are the same. I also show that the prize dissipation ratio for each player is less than or equal to the minimum of the players' probabilities of winning at the Nash equilibrium and thus never exceeds a half. Then I examine how the equilibrium effort ratio, the prize dissipation ratios, and the players' equilibrium effort levels respond when the players' valuations for the prize or their abilities change.     

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)     

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)     

SLEEPING WITH THE ENEMY: THE ECONOMIC COST OF INTERNAL ENVIRONMENTAL CONFLICTS

This paper extends the literature on collective rent‐seeking by introducing the possibility that a competing group may be a subset of another. We develop a model that incorporates the potential for some individuals to be party of both sides of a conflict, which creates interdependence of payoffs. Results indicate that strategic individual behavior, and the resulting rent dissipation, is affected by the relative size of the groups. We conduct an experimental test of the model and find that observed laboratory behavior corresponds well with the game‐theoretic comparative‐static predictions. (JEL C72, C9, Q5, D74)     

ENDOGENOUS TIMING IN CONTESTS WITH DELEGATION

We study two‐player contests in which each player hires a delegate, and the delegates decide endogenously when to expend their effort. First, we look closely at the delegates' decisions on when to expend their effort, given contracts between the players and the delegates, and look at the players' decisions on their contracts. Then, we compare the outcomes of the endogenous‐timing framework with those of the simultaneous‐move framework. We show that the higher‐valuation player offers her delegate greater contingent compensation than her opponent, the delegate of the higher‐valuation player chooses his effort level after observing his counterpart's, the equilibrium expected payoff of the delegate of the higher‐valuation player is greater than that of his counterpart, and economic rent for each delegate exists. We show that, in the endogenous‐timing framework, each player offers her delegate better contingent compensation, each delegate's expected payoff is greater, and each player's expected payoff is smaller, as compared with the simultaneous‐move framework. (JEL D72)     

CONTESTS WITH STOCHASTIC ABILITIES

We consider the properties of perfectly discriminating contests in which players' abilities are stochastic, but become common knowledge before efforts are expended. Players whose expected ability is lower than that of their rivals may still earn a positive expected payoff from participating in the contest, which may explain why they participate. We also show that an increase in the dispersion of a player's own ability generally benefits this player. It may benefit or harm his rival but cannot benefit the rival more than it benefits himself. We also explore the role of stochastic ability for sequential contests with the same opponent (multibattle contests) and with varying opponents (elimination tournaments) and show that it reduces the strong discouragement effects and holdup problems that may otherwise emerge in such games. High own ability dispersion selects such players into the contest and favors them in elimination contests. ( JEL D72, D74)     

HIERARCHICAL TRADE

Commodity trading is typically organized hierarchically: Large‐scale trade takes place at the global price system while individuals trade at local price systems within their countries. Agencies or trading houses establish the link between these different market places. In this paper, we devise a framework to study this type of hierarchical trade. We identify the free trade and the autarky equilibrium as polar cases. We show that no other two‐stage market equilibria exist if the commodity space is two‐dimensional. An example demonstrates that other, so‐called intermediate equilibria exist for three‐dimensional commodity spaces. We then provide an explicit construction of special classes of intermediate equilibria. Moreover, we study the consequences when some countries control the agency that organizes trade at the global level and we analyze the role of international goods arbitrage. Finally, we show that profit‐maximizing agencies may not promote free trade outcomes. (JEL D43, D50, F10)     

SIGNAL EXTRACTION AND RATIONAL INATTENTION

In this paper we examine the implications of two theories of informational frictions, signal extraction (SE) and rational inattention (RI), for optimal decisions and economic dynamics within the linear‐quadratic‐Gaussian (LQG) setting. We first show that if the variance of the noise and channel capacity (or marginal information cost) is fixed exogenously in the SE and RI problems, respectively, the two environments lead to different policy and equilibrium asset pricing implications. Second, we find that if the signal‐to‐noise ratio and capacity in the SE and RI problems are fixed, respectively, the two theories generate the same policy implications in the univariate case, but different policy implications in the multivariate case. We also show that our results do not depend on the presence of correlation between fundamental and noise shocks. We then discuss the applications to macroeconomic models of permanent income and price‐setting. (JEL C61, D81, E21)     

The robustness of ‘enemy-of-my-enemy-is-my-friend’ alliances

We examine a three-player, three-stage game of alliance formation followed by multi-battle conflict. There are two disjoint sets of battlefields, each of which is associated with a player who competes only within that set. The common enemy competes in both sets of battlefields. An ‘enemy-of-my-enemy-is-my-friend’ alliance forms when the two players facing the common enemy agree on a pre-conflict transfer of resources among themselves. We examine the case in which the players may commit to binding ex post transfers (alliances with full commitment) and the case in which ex post transfers are not feasible (self-enforcing alliances). Models that utilize the lottery contest success function typically yield qualitatively different results from those arising in models with the auction contest success function. However, under both contest success functions, alliances with full commitment result in identical alliance transfers for all parameter configurations, and self-enforcing alliances yield identical transfers over a subset of the parameter space. Our results, thus, provide a partial robustness result for ‘enemy-of-my-enemy-is-my-friend’ alliances.     

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)     

TO DETER OR TO MODERATE? ALLIANCE FORMATION IN CONTESTS WITH INCOMPLETE INFORMATION

We consider two players' choice about the formation of an alliance ahead of conflict in a framework with incomplete information about the strength of the potential ally. When deciding on alliance formation, players anticipate the self‐selection of other players and the informational value of own and other players' choices. In the absence of these signaling effects, strong players have an incentive to stand alone, which leads to a separating equilibrium. This separating equilibrium can be destabilized by deception incentives if beliefs are updated on the basis of endogenous alliance formation choices. Weak players may find it attractive to appear strong in order to deter competitors from positive effort choices. Strong players may find it attractive to appear weak in order to give their competitors a false sense of security and then beat them with little effort. Moreover, appearing weak allows players to free‐ride when alliances are formed. (JEL D72, D74)