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

digging for golden carrots an analysis of research tournaments contracting for research is often infeasible because research inputs are unobservable and research outcomes cannot be verified by a court sponsoring a research tournament can resolve these problems a model is presented in which contestants compete to find the innovation of highest value to the tournament sponsor the winner receives a prespecified prize the tournament game has a unique subgame perfect equilibrium free entry is not optimal because equilibrium effort by each researcher decreases in the number of contestants an optimally designed research tournament balances the probability of overshooting the first best quality level against the probability of falling short copyright 1995 by american economic association

the beauty of bigness on optimal design of multi winner contests abstract this paper examines the variation in total effort expended by participants when prizes are awarded in a grand contest as opposed to a number of subcontests when contestants are homogeneous under a mild and plausible condition regular contest technology a grand contest generates more effort than any set of subcontests when no restrictions are placed on the contest technology the results further demonstrate an increasing return to scale property such that each individual responds to a proportional increase in the number of contestants and the number of each prize by increasing individual effort therefore when a collection of identical subcontests forms a grand contest the total effort always increases and the grand contest leads to a higher rent dissipation rate our results apply to a wide variety of competitive activities such as high profile sports e g diving and gymnastics in the olympic games the internal labor market and the quota system for public resource allocation

contest design and optimal endogenous entry this paper derives the effort maximizing contest rule and the optimal endogenous entry in a context where potential participants bear fixed entry costs the organizer is allowed to design the contest under a fixed budget with two strategic instruments he sets the value of the prize purse and arranges a monetary transfer entry subsidy or fee for each participating contestant in other words the budget can either be used to subsidize participation or an entry fee can be charged to fund the prize purse the results show that the optimally designed contest attracts exactly two participating contestants in its unique subgame perfect equilibrium when there is a positive fixed entry cost and extracts all the surplus from participating contestants the study also shows that the direction and amount of the monetary transfer depend on the magnitude of the entry cost the contest organizer subsidizes entry when contestants bear substantial entry costs but charges an entry fee to fund the prize purse whenever the entry cost is sufficiently low

using contests to allocate pollution rights in this paper we advocate a new initial allocation mechanism for a tradable pollution permit market we outline a permit allocation contest pac that distributes permits to firms based on their rank relative to other firms this ranking is achieved by ordering firms based on an observable external action where the external action is an activity or characteristic of the firm that is independent of their choice of emissions in the tradable permit market we argue that this mechanism has a number of benefits over auctioning and grandfathering using this mechanism efficiently distributes permits allows for the attainment of a secondary policy objective and has the potential to be more politically appealing than existing alternatives

contests with multiple rounds this paper studies contests where players have the flexibility to add to their previous efforts after observing their rivals most recent effort in an intermediate stage it is found that 1 contrary to previous findings the stackelberg outcome where the underdog leads and the favorite follows cannot be an equilibrium 2 there are multiple subgame perfect equilibria all occurring on the underdog s usual one shot reaction function in between and including the one shot cournot nash and stackelberg outcome with the favorite leading 3 the total equilibrium effort is typically greater than or equal to what a one shot cournot nash play would predict and 4 in settings where players can choose whether or not to disclose their early actions to the rival both the favorite and the underdog disclose in equilibrium applications in sports lobbying and r d races are discussed

election goals and the allocation of campaign resources this paper compares the equilibrium behavior and outcomes in a model of two party competition for legislative seats under two different assumptions about the parties goals 1 parties maximize the expected number of seats won and 2 parties maximize the probability of winning a majority of the seats the two goals may lead to qualitatively different behavior and studying the differences yields insights into the relationship between the goals and the role of assymetries between the parties

asymmetric all pay auctions with incomplete information the two player case abstract we prove existence and uniqueness of bayesian equilibrium for a class of generally asymmetric all pay auctions with incomplete information due to its importance in applications some prominence is given to the first price all pay auction for which a detailed characterization of equilibrium and an approximation to equilibrium of its well studied complete information version are supplied furthermore we relate our uniqueness result to the well known multiplicity of equilibria in the war of attrition second price all pay auction which emerges as a limit point of the class of two player auction games considered journalof economic literature classification numbers d44 c62 c72

the optimal prize structure of symmetric tullock contests we show that the optimal prize structure of symmetric n player tullock tournaments assigns the entire prize pool to the winner provided that a symmetric pure strategy equilibrium exists if such an equilibrium fails to exist under the winner take all structure we construct the optimal prize structure which improves existence conditions by dampening efforts if no such optimal equilibrium exists no symmetric pure strategy equilibrium induces positive efforts

endogenous timing in contests with delegation i introduction contests with delegation where each player hires a delegate to expend effort or resources on the player s behalf to win a prize are common 1 an example is litigation between a plaintiff and a defendant in which each litigant hires an attorney who expends his effort to win the lawsuit on behalf of his client another example is a rent seeking contest in which each firm hires a lobbyist who expends his effort to acquire a monopoly or a procurement contract from the government on behalf of his client yet another example is a patent contest in which each firm hires a group of independent researchers or university professors who conduct research to obtain a patent on behalf of their employer delegation is attractive to players because they each can use superior ability by hiring a delegate with more ability than herself and achieve strategic commitments through delegation in such contests with delegation we believe delegates decide endogenously when to expend their effort after signing delegation contracts indeed pursuing their self interest the delegates may well endogenize the order of their moves and communicate it with each other before they expend their effort we believe also that players take it into account when designing their contracts for the delegates that the delegates will endogenize the order of their moves it is these ideas that motivate this paper accordingly the purpose of this paper is to systematically study contests with delegation in which delegates decide endogenously when to expend their effort after signing delegation contracts and before they expend their effort we study two player contests with delegation focusing on not only the equilibrium delegation contracts between players and their delegates but also the equilibrium orders of the delegates moves specifically we set up and analyze the following three stage game in the first stage two players each hire a delegate and they simultaneously announce their contracts written with their delegates each player s contract specifies how much her delegate will be paid if he wins the contest and how much if he loses it in the second stage each delegate decides when to expend his effort and the delegates announce their decisions simultaneously in the third stage the delegates expend their effort according to their decisions in the second stage to win the prize on behalf of their employers we show that in equilibrium the delegate hired by the higher valuation player chooses his effort level after observing his counterpart s and his expected payoff is greater than that of his counterpart this advantage of the delegate of the higher valuation player can be explained by the fact that his employer the higher valuation player offers better contingent compensation as it will be defined in section ii to him than the lower valuation player does to her delegate we compare the outcomes of the endogenous timing framework the three stage game presented above with those of the simultaneous move framework the game which is the same as the three stage game with the exception that the delegates choose their effort levels simultaneously and this order of their moves is given exogenously an interesting result is that each player offers her delegate a better contract in the endogenous timing framework than in the simultaneous move framework another interesting result is that unless the valuation for the prize of the higher valuation player is significantly greater than that of the lower valuation player then each delegate s expected payoff is greater in the endogenous timing framework than in the simultaneous move framework whereas each player s expected payoff is less in the endogenous timing framework than in the simultaneous move framework in summary pursuing their self interest the delegates decide endogenously when to expend their effort given contracts between the players and the delegates

how to split the pie optimal rewards in dynamic multi battle competitions abstract multi battle competitions are ubiquitous in real life in this paper we examine the effort maximizing reward design in sequentially played multi battle competitions between two players the organizer has a fixed prize budget and rewards players contingent on the number of battles they win in a three battle contest a full spectrum of contest technologies in the tullock family is accommodated we find that the optimal design varies with the discriminatory power of the contest technology in particular when it is in the low range winner take all is optimal for the intermediate range as discriminatory power increases the optimal prize structure evolves continuously from winner take all to the proportional division rule due to the need to mitigate the growing momentum discouragement effect for the high range a wide span of prize structures extracts full surplus and is thus optimal several robustness checks confirm that mitigating the momentum discouragement effect is essential for effort maximizing prize design in dynamic multi battle contests

bid costs and endogenous bid caps we study contests where several privately informed agents bid for a price all bidders bear a cost of bidding that is an increasing function of their bids and moreover bids may be capped we show that regardless of the number of bidders if agents have linear or concave cost functions then setting a bid cap is not profitable for a designer who wishes to maximize the average bid on the other hand if agents have convex cost functions i e an increasing marginal cost then affectively capping the bids is profitable for a designer facing a sufficiently large number of bidders

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

search duplication in research and design spaces exploring the role of local competition a lack of sufficient diversification in research strategies has been identified as an important problem for delegated research we show that this problem can be solved by local competition such as bribery lobbying rent seeking competition at the patent office among players who apply the same search strategies or develop the same design such competition can restore full efficiency in the non cooperative equilibrium local competition interacts with the choice of whether to cluster or diversify and rather than adding a further inefficiency to the existing ones it eliminates inefficiency the results are robust and hold under simultaneous search strategy choices as well as for sequential choices

do tournaments have incentive effects much attention has been devoted to studying models of tournaments or situations in which an individual s payment depends only on his or her output or rank relative to that of other competitors academic interest derives from the fact that under certain sets of assumptions tournaments have desirable normative properties because of the incentive structures they provide our paper uses nonexperimental data to test whether tournaments actually elicit effort responses we focus on professional golf tournaments because information on the incentive structure prize distribution and measures of individual output players scores are both available we find strong support for the proposition that the level and structure of prizes in pga tournaments influence players performance

dissipation of contestable rents by small numbers of contenders the theory of rent seeking with its origins in the observations of gordon tullock 1967 or to use jagdish bhagwati s 1982 proposed term the theory of directly unproductive profit seeking activities is concerned with the potentially adverse effects on resource allocation of incentives to cap ture and defend artificially contrived rents and transfers the scope for so cial loss proposed by the theory derives from the relation between the value of a contestable prize and the value of the resources attracted into the con test to determine the beneficiary of the prize underlying this social loss is a specification of how rational behavior by optimizing agents links the value of the prize sought to the resources expended it has been traditional to assume competitive behavior in describing the activities of lobbying and influence seeking then if some further condi tions are satisfied l the total value of the resources expended precisely equals the value of the prize sought so dissipation is complete 2 conse quently the social cost associated with contestability of a rent can be in ferred from the value of the rent itself and the detailed and hard to come by information on individual outlays made in the course of the contest be comes unnecessary by basing their analyses on competitive dissipation contributors to the rent seeking literature see the review by robert tollison 1982 have been able to presume that the observed value of a contested rent is an exact measure of the associated social cost of monopoly power or regu lation similarly in the trade theoretic literature where the rights contested are to quota premia or revenues from trade taxes krueger 1974 bhagwati

the economics of invention incentives patents prizes and research contracts though public intervention in the market for research is virtually universal economists have paid surprisingly little attention to the choice of the form of research incentive in a given market structure many studies concentrate on patents but any assumption of their superiority over other incentives has been founded on intuition rather than on formal analysis in this paper i analyze the choice between three of the most common alternative means of public intervention in the research market namely patents prizes and direct contracting for research services i show why and under what conditions any one of the three may be preferred by a social welfare maximizing administrator in a competitive economy using a model that for the first time pays explicit attention to differences in the informational roles of each of these alternatives in the extensive literature on the economics of patents see arnold plant 1934 fritz machlup 1958 charles taylor and z a silberston 1973 morton kamien and nancy schwartz 1975 and f m scherer 1977 for valuable surveys formal analysis weighs the benefits of patents as a solution to the market failure associated with the inappropriability of knowledge against the welfare cost due to the restriction on the use of the knowledge generated and this tradeoff is optimized by patent life adjustment in william nordhaus 1969 scant analytical attention is paid to alternative incentive mechanisms an exception is ben yu 1981 who considers the role of prior contracting for inventions but as many writers for example dan usher 1964 yoram barzel 1968 joseph stiglitz 1969 carole kitti 1973 glenn loury 1979 partha dasgupta and stiglitz 1980a have pointed out in various contexts the incentive offered by an unlimited patent to competitive researchers may be excessive due to the common pool problem discussed further in section i below if the patent administrator and researchers share the same information as implicitly assumed in previous models then the patent life limitation can be adjusted to provide the optimal patent incentive given the common pool problem but in all such models patents would not be chosen in a fully optimized fiscal system researchers and the administrator are assumed to have identical information about the shadow price of potential inventions a patent is just a means of turning this shadow price into a monetary reward but monetary compensation can instead be offered directly to researchers by the state assuming that patent revenues incur a higher deadweight loss than an equivalent amount of public funds financed by less distortionary means for example a minimally efficient tax system appropriate prizes or government contracts are socially preferable to patents with optimal lives if the patent is ever to be the optimal incentive mechanism for research it must possess advantages not captured in existing models informal discussions of patents emphasize their informational role to include the latter as a justification for decentralized invention incentives i incorporate an ex ante imbalance of information about costs and benefits of research in the model presented in section ii but this alone is not quite enough it is further necessary to specify that the terms of the award must be fixed before department of economics economic growth center box 1987 yale station yale university new haven ct 06520 i thank with the usual caveat marguerite alejandro wright cindy arfken martin baily nuong brennan steven englander robert evenson richard levin richard nelson susan rose ackerman denis wright and two referees for assistance of various kinds

influencing rent seeking contests this paper shows that a policy that uniformly increases contestants effort costs can lead to an increase in total effort in asymmetric settings this levels the playing field and therefore encourages weaker players who otherwise would have stayed out to enter paradoxically a contest designer whose only objective is to maximize total effort may thus wish to make rent seeking more difficult these results suggest that the often lamented bureaucratic red tape might in fact be a rational response to the problem of attracting lobbyists to participate in a contest

optimal prize rationing strategy in all pay contests with incomplete information abstract a contest organizer e g a government regulatory agency is endowed with the capacity to provide unlimited homogeneous prizes e g medals that he can use to incentivize contestants to exert productive effort in an all pay auction with incomplete information each agent at most wins one prize we study the optimal number of prizes the organizer should grant in order to induce maximal expected total effort or expected highest effort from agents both are single peaked under mild regularity conditions when players abilities follow a family of beta distributions expected highest effort maximization requires a smaller set of prizes to be awarded for both goals the optimal number of prizes weakly increases when the pool of contestants expands or contestant quality improves

a model of a team contest with an application to incentives under list proportional representation abstract we develop a model of a team contest for multiple indivisible prizes team members exert costly effort to improve their team s success we analyze two intrateam allocation rules under a list rule prizes are allocated according to a predetermined list under an egalitarian rule prizes are allocated according to a fair lottery we show that which allocation rule maximizes team success depends on the degree of complementarity between members efforts and the convexity of the individual cost of effort function we then apply the model to the context of elections under proportional representation with both open and closed lists we derive conditions under which closed lists generate stronger incentives than open lists our results offer a rationale for the lack of evidence on the negative incentive effects of closed lists

testing the theory of tournaments an empirical analysis of broiler production broiler chickens are raised by contract growers whose rewards depend explicitly upon relative performance we use data on the performance of broiler producers facing both tournament and linear performance evaluation compensation structures to test three predictions from the theory of tournaments that changes in the level of prizes that leave prize differentials unchanged will not affect performance that in mixed tournaments more able players will choose less risky strategies and that tournament organizers will attempt to handicap players of unequal ability or reduce mixing to avoid the disincentive effects of mixed tournaments our evidence is consistent with each prediction

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

on requiring the durable goods monopolist to sell abstract requiring a monopolist to sell its output rather than renting it my lead to beneficial output adjustments or harmful quality adjustments in a durable goods model we show that requiring sales decreases welfare in only a small fraction of cases but it strictly increases welfare in a majority of cases

the assessment the economics of sport the study of sports economics has expanded rapidly in recent years in response to significantly increased demand for sport itself for economic analysis relevant to commercial litigation in sport for lively teaching material in schools and universities and for research into the incentive properties of sporting contests while much of the literature has focused on the issue of competitive balance and how to achieve it there have still been relatively few studies that apply the lessons of the economic theory of contests to the analysis of sports there remain huge opportunities both to develop our theoretical understanding of incentive mechanisms in sport and to conduct empirical research in the operation of incentives in sporting contests copyright 2003 oxford university press

political culture and discrimination in contests abstract many economic and political decisions are the outcome of strategic contests for a given prize the nature of such contests can be determined by a designer who is driven by political considerations with a specific political culture the main objective of this study is to analyze the effect of political culture and of valuation asymmetry on discrimination between the contestants the weights assigned to the public well being and the contestants efforts represent the political culture while discrimination is an endogenous variable that characterizes the mechanism allocating the prize we consider situations under which the optimal bias of the designer is in favor of the contestant with the larger or smaller prize valuation and examine the effect of changes in the political culture and in valuation asymmetry on the designer s preferred discrimination between the contestants focusing on the two most widely studied types of contest success functions deterministic all pay auctions and logit csfs we show that an all pay auction is always the preferred csf from the point of view of the contest designer this result provides a new political economic micro foundation to some of the most commonly used models in the contest literature

disclosure policy in a multi prize all pay auction with stochastic abilities this paper investigates whether a contest organizer should disclose private information about bidders abilities in a multi prize all pay auction bidders abilities are randomly distributed and observed by the contest organizer the organizer decides whether to disclose this information publicly we find that concealing the information elicits higher expected total effort regardless of the distribution of abilities in addition we find that the rent dissipation rate of the contest does not depend on the disclosure policy

quitters never win the adverse incentive effects of competing with superstars internal competition may motivate worker effort yet the benefits of competition may depend critically on workers relative abilities large skill differences may reduce efforts i use panel data from professional golf tournaments and find that the presence of a superstar is associated with lower performance on average golfers first round scores are approximately 0 2 strokes worse when tiger woods participates relative to when woods is absent the overall tournament effect is 0 8 strokes the adverse superstar effect varies with the quality of woods s play there is no evidence that reduced performance is attributable to media attention intensity or risky strategy adoption

it takes two to tango equilibria in a model of sales we show that the varian model of sales with more than two firms has two types of equilibria a unique symmetric equilibrium and a continuum of asymmetric equilibria in contrast the 2 firm game has a unique equilibrium that is symmetric for the n firm case the asymmetric equilibria imply mixed strategies that can be ranked by first order stochastic dominance this enables one to rule out asymmetric equilibria on economic grounds by constructing a metagame in which both firms and consumers are players the unique subgame perfect equilibrium of this metagame is symmetric

disclosure policies in research contests with stochastic entry abstract this paper models research contests as an all pay auction with stochastic entry and analyzes the effect of disclosing the actual number of participants on the expected winning bid i find that the classic disclosure irrelevance principle on expected revenue does not extend to the ranking on expected winning bid the ranking on expected winning bid crucially depends on the number of potential bidders participation probabilities and the distribution of bidders valuations when there are more than two potential bidders fully concealing the actual number of participants elicits a higher expected winning bid if potential bidders have low participation probabilities whereas the rank reverses if bidders have high participation probabilities and high chances of being high types

rent seeking with regretful agents theory and experiment abstract we investigate both theoretically and experimentally the role that information disclosure has on behavior in all pay environments in which all agents must exert costly effort but only the winner is rewarded through the lens of all pay auctions we show that bidders who have regret concerns when they lose an auction may alter their bids whether or not information about the winning bid is disclosed all losing bidders regret not bidding 0 however when feedback on the winning bid is provided those bidders who lost at an affordable price may regret not bidding more we show that the former effect causes bidders to lower their bids while the latter effect causes bidders to raise their bids our experimental results indicate overbidding whether or not the winning bid is disclosed to losing bidders however disclosing the winning bid leads to even more aggressive bidding increases revenues decreases the frequency of dropouts and also leads to more efficient allocations thus our results show that information disclosure is a powerful tool that mechanism designers may wish to exploit to extract more rents in all pay environments

endogenous timing in general rent seeking and conflict models we examine simultaneous versus sequential choice of effort in a two player contest the timing of moves determined in a preplay stage prior to the contest subgame as well as the value of the prize is allowed to be endogenous contrary to endogenous timing models with an exogenously fixed prize the present paper finds the following 1 players may decide to choose their effort simultaneously in the subgame perfect equilibrium spe of the extended game 2 the spe does not need to be unique in particular there is no unique spe with sequential moves if the direct costs of effort are zero 3 symmetry among players does not rule out incentives for precommitment to effort locally away from the cournot nash level 4 finally there may be no correlation between win probability and strategic incentives in our framework a finding most central in the analysis of fixed prize contests

uniqueness and existence of equilibrium in auctions with a reserve price abstract we prove existence and uniqueness of equilibrium for a general class of two player bidding games we apply our results to the first price auction the combination of first and second price auctions the war of attrition the all pay auction as well as combinations of the latter two auction forms we also treat the first price auction without risk neutrality our results deal with the asymmetric affiliated common values environment in the case where signals are independent our results apply to all equilibria when signals are not independent our uniqueness results hold in the class of nondecreasing strategy equilibria journal of economic literature classification number d44

the optimal allocation of prizes in contests we study a contest with multiple not necessarily equal prizes contestants have private information about an ability parameter that affects their costs of bidding the contestant with the highest bid wins the first prize the contestant with the second highest bid wins the second prize and so on until all the prizes are allocated all contestants incur their respective costs of bidding the contest s designer maximizes the expected sum of bids our main results are 1 we display bidding equlibria for any number of contestants having linear convex or concave cost functions and for any distribution of abilities 2 if the cost functions are linear or concave then no matter what the distribution of abilities is it is optimal for the designer to allocate the entire prize sum to a single first prize 3 we give a necessary and sufficient conditions ensuring that several prizes are optimal if contestants have a convex cost function

auctionin entry into tournaments a research tournament model with heterogeneous contestants is presented for a large class of contests the optimal number of competitors is two this insight makes designing the tournament easier and highlights the importance of selecting highly qualified contestants while customary uniform price and discriminatory price auctions are intuitively appealing mechanisms for solving this adverse selection problem in practice they generally will not be efficient mechanism for selecting contestants instead we propose an alternative auction format that is equally simple to implement and efficiently selects the most qualified contestants to compete regardless of the form of contestant heterogeneity

optimal design of research contests procurement of an innovation often requires substantial effort by potential suppliers motivating effort may be difficult if the level of effort and quality of the resulting innovation are unverifiable if innovators cannot benefit directly by marketing their innovations and if the buyer cannot extract up front payments from suppliers we study the use of contests to procure an innovation in such an environment an auction in which two suppliers are invited to innovate and then bid their prizes is optimal in a large class of contests if contestants are asymmetric it is optimal to handicap the most efficient one

risk taking in contests and the role of carrots and sticks i introduction when individuals compete for promotions bonuses or other rewards tied to their relative performance ranking vis a vis other contestants competition is likely to drive not just work effort but where imperfect monitoring permits other choices at the contestants discretion in this article we ask how rank dependent compensation influences attitudes toward risk or the choice of variance of output when contestants have opportunities to influence this aspect of their output distribution unlike previous literature we assume that it is costly for contestants to alter the variance of output and that identical contestants simultaneously choose both the mean of their output distribution i e work effort and its variance our analysis emphasizes the importance of the number of players and symmetry or lack thereof of payoffs on contestants incentives we find that contestants will engage in risk seeking increasing the variance of their output distribution in contests among three or more players when the payoff structure offers a greater prize for ranking first than the penalty for ranking last as happens in winner take all contests if the tournament organizer or sponsor values the aggregate output of the contestants as is typically assumed in labor market tournaments this risk seeking behavior is inefficient because it is costly but does not increase the expected output however we argue that many contests such as the research and development tournaments first modeled by taylor 1995 may be characterized by an organizer who cares only or primarily about the highest output achieved by a single contestant e g the best submission received in such cases the organizer may benefit from costly risk taking among contestants we show that three payoff levels a prize to the contestant ranked first a penalty to the contestant ranked last and a common intermediate payoff to all others are sufficient to achieve any combination of effort and variance of output that the organizer wishes to induce among contestants so long as the desired output variance does not exceed that which results from a winner take all prize structure therefore the sponsor s problem can be characterized as choosing the optimal mean and variance of the output distribution given the contestants costs of influencing the mean and variance of output in this way our model provides an explanation for the importance of both carrots prizes and sticks penalties in competitive settings only through the combined use of both can a contest organizer determine the effort and the variance of output chosen by contestants and doing so is necessary to achieve optimal performance from contests since the pioneering work of lazear and rosen 1981 nalebuff and stiglitz 1983 o keeffe viscusi and zeckhauser 1984 and others rank order tournaments or contests have been used to model incentives in a variety of economic settings in particular executive compensation has frequently been modeled as a tournament in which low level executives are motivated by the prospect of climbing the corporate ladder and obtaining the large salaries attendant to top ranking executives as in rosen 1986 and bognanno 2001 similarly the behavior of investment fund managers who compete for top fund rankings has been modeled as a tournament by brown harlow and starks 1996 taylor 1995 developed a model of research tournaments in which contestants search for an innovation and the best innovation submitted to the sponsor wins a prize the distinguishing feature of a tournament or contest is that contestants are paid based on the rank of their output relative to others rather than the level of output prize levels are set in advance and competition to win generates the incentive to exert effort to increase output lazear and rosen 1981 showed that rank order tournaments can provide an efficient incentive framework in a labor market setting when workers are risk neutral

competitive burnout theory and experimental evidence abstract we examine equilibrium selection in a two stage sequential elimination contest in which contestants compete for a single prize this game has a continuum of equilibria only one of which satisfies the coalition proof nash equilibrium cpne refinement that equilibrium involves burning out by using all of one s resources in the first stage it is pareto dominated by many other equilibria we find that cpne predicts well when four people compete but not when eight people compete for two second stage spots using a cognitive hierarchy ch framework we show that when the number of players and the mean number of thinking steps are large the ch prediction involves burning out this provides a partial explanation of our results we also develop a formal argument as to why cpne logic is more compelling with more players we conclude that more competition leads to higher bids and that burning out is indeed a competitive phenomenon

runner up patents is monopoly inevitable exclusive patents sacrifice product competition to provide firms incentives to innovate we characterize an alternative mechanism whereby later inventors are allowed to share the patent if they discover within a certain time period of the first inventor these runner up patents increase social welfare under very general conditions furthermore we show that the time window during which later inventors can share the patent should become a new policy tool at the disposal of the designer this instrument will be used in a socially optimal mix with the breadth and length of the patent and could allow sorting between more or less efficient firms

the incentive effect of coarsening the competition structure in a tournament the incentive effect of coarsening the competition structure in a tournament is studied by coarsening the competition structure we mean that coarser performance measure is used while finer information is available examples include letter grades or grade classes when finer numeric grades are available coarsening the competition structure has two countervailing incentive effects while it reduces the likelihood that marginal effort changes the result the reward change will be bigger once the result is changed we provide a sufficient condition on the performance distribution for the reduction of work incentive by coarsening log concavity of the density

suspense dynamic incentives in sports contests in a dynamic model of sports competition if spectators care only about contestants efforts incentive schemes depending linearly on the final score difference dominate rank order schemes based only on who wins if spectators also care about suspense defined as valuing more contestants efforts when the game is closer rank order schemes can dominate linear score difference schemes and this will be the case when the demand for suspense is sufficiently high under additional assumptions we show that the optimal rank order scheme dominates a broad class of incentive schemes sport contestants can earn substantial financial prizes total prize money at wimble don topped 10 million for the first time in 2005 the professional golf association has distributed approximately 250 million in prize money across 48 events in the pga tour even in less professional sports prize money plays an important role nearly 21 million in prize money was awarded in international track and field competitions in 2004 interestingly prize money is typically allocated on the basis of who wins and who loses more informative measures of performance such as score differences rarely matter even though they are readily available when there are several contestants in a sporting event rewards depend on who wins the most games round robin tourna ment or on the sequence of games won elimination tournament total scores and other performance measures matter only in terms of determining who the winner is not how much the winner gets although for superstar athletes prize money pales in comparison with income from sponsorship deals only about 6 million of tiger woods income of close to 90 million in 2004 was prize money sponsorship money can depend on factors such as charisma and star power other than athletic perform ance so prize money is still the main provider of incentives for efforts in a given sports event likewise in recent years contracts for players in some team sports are loaded with incentive clauses that often take on a strong piece rate flavour e g salaries for batters depending on the batting average in baseball but financial incentives for team efforts remain largely independent of relative performance measures such as score differences why do win lose rank order incentives dominate in the design of financial incentives in sports especially in individual sports the literature on optimal design of rank order tournaments that began with lazear and rosen 1981 explains how tournaments provide incentives for efforts however the literature has not shed much light on when rank order incentive schemes are preferred to schemes based on other relative performance measures particularly when the agents are risk neutral prendergast 1999 pp 36 7 reviews several reasons for using tournaments but it remains unclear why prizes in sporting events depend only on rank order of scores and not on scores themselves holmstrom 1982 casts doubt this article was originally titled suspense it was first presented at the memorial conference for sherwin

incentivizing r d prize or subsidies abstract this paper studies the optimal design of r d contests a sponsor e g the us department of defense or the world health organization wants to improve the quality of the winning products to do so it partitions its budget between two schemes an inducement prize and efficiency enhancing subsidies to the firms competing in the contest prizes and subsidies have different functions and they provide complementary incentives in the optimally designed contest subsidies increase while the prize decreases if the innovation process is more challenging further sensible conditions are identified under which the optimal contest implements either a handicapping scheme by preferentially subsidizing the underdog or a national champion scheme by favoring the favorite our analysis yields a number of useful implications and sheds light on an array of r d incentive schemes such as the dod s design competitions and vaccine development incentives

coordination in split award auctions we analyze split award procurement auctions in which a buyer divides full production between two suppliers or awards all production to a single supplier and suppliers have private cost information an intriguing feature of split awards is that the equilibrium bids are implicitly coordinated because a split award price is the sum of offered split prices each supplier can unilaterally veto a split award by bidding very high for the split the need to coordinate is reflected in a split price that does not vary with private information we also explore conditions under which split award auctions may be preferred to winner take all auctions

do polls create momentum in political competition abstract we explore how public opinion polls affect candidates campaign spending in political competition generally polls lead to more asymmetric behavior under a majority rule there always exists an equilibrium in which the initially more popular candidate invests more in the campaign and thereby increases her lead in expectation polls create momentum when campaigning is very effective and the race is very close a second type of equilibrium may exist the trailing candidate outspends and overtakes his opponent regardless of the type of equilibrium polls have a tendency to decrease expected total campaigning expenditures by amplifying ex ante asymmetries between candidates and thus defusing competition when candidates care also for their vote share in addition to having the majority candidates incentives crucially depend on the distribution of voters candidate preferences

optimal lottery design for public financing this article develops a model of optimal lottery design for public financing on the assumption that economic agents view buying lottery tickets as a form of entertainment given that lotteries are optimally designed it offers two findings 1 the fundraising potential of a lottery is independent of its type specifically of whether it is a fixed prize type or a pari mutuel and 2 the ratio of the optimal winning prize amount in each prize class to total lottery sales is equalised to the elasticity of demand for lottery ticket purchases with respect to the winning prize in each prize class

multi stage sequential all pay auctions abstract we study multi stage sequential all pay contests auctions where heterogeneous contestants are privately informed about a parameter ability that affects their cost of effort we characterize the perfect bayesian equilibrium of these contests and analyze the effect of the number of contestants and their types on the contestants expected highest effort

the effort maximizing contest with heterogeneous prizes we establish the effort maximizing rule of allocating heterogeneous prizes when contestants privately observe their effort efficiencies with ex ante symmetric players and increasing virtual effort efficiency an all pay auction maximizes the total expected effort

tournament rewards and risk taking this article considers a lazear rosen tournament model where agents can influence both the spread of their output distribution risk taking and its mean the unique equilibrium induces excessive risk taking and a low level of effort by modifying the tournament to give the highest prize to the agent with the most moderate output a low level of risk taking and high level of effort can be sustained as an equilibrium the first result can be useful to understand the relative performance evaluation puzzle of executive compensation and the second result can be useful to understand puzzling workplace norms promoting mediocrity

caps in sequential contests i introduction in many competitions we can often observe situations where severe constraints are imposed on contestants for example in the u s electoral campaign there is a specific maximum campaign contribution that a single agent can make to a candidate 1 in sports where equipment plays a major role e g sailing motor races etc explicit or implicit technological constraints are imposed on the allowed equipment also several sports leagues e g the national basketball association nba implement a salary cap which places a limit on the total amount of money a team can spend on players salaries salary caps are clearly binding and teams are sometimes forced to trade expensive players in order to make place for other needed team members the usual reason for applying salary caps is that they facilitate even competition between small and large city teams otherwise large city teams could pay more buy the best talent and ultimately destroy any semblance of competition in the league the goal of caps imposed by designers of competitions is to create what we call a competitive balance so that many players have a chance to win and not necessarily the strongest ones in addition if the contest is more competitively balanced the uncertainty of the outcome is higher and therefore the contest is more attractive furthermore competitive balance may lead to an improvement of the expected total performance of all the players rather than just the performance of the top player several other ways have been suggested to enhance the competitive balance in contests for example baye kovenock and de vries 1993 showed that in all pay auctions contests by excluding the strongest player the player with the highest value of winning the contest becomes more competitively balanced and then the players expected total bid may increase moldovanu and sela 2001 found that in all pay auctions under incomplete information when cost functions are convex several positive prizes may be optimal for a designer who wishes to maximize the expected total bid in other words by increasing the number of the prizes the chances of the players with relatively low values of winning to win one of the prizes increase and therefore these players will increase their efforts accordingly cohen kaplan and sela 2008 studied all pay auctions with effort dependent rewards under incomplete information and demonstrated that when the designer maximizes the total bid effort and when there is a sufficiently large number of contestants the optimal reward decreases in the contestants bid this means that a designer will offer higher prizes to the players with relatively low values of winning those who exert lower efforts than to the players with relatively high values of winning those who exert higher efforts such a distribution of prizes balances the bids submitted by the players with high and low values of winning we focus here on the role of bid caps to enhance the competitive balance in contests relatively weak players players with low abilities or low values of winning usually exert low efforts which are lower than the level of the bid cap imposed by a designer in a contest with a bid cap if these players exert an effort that is equal to the bid cap they will have a higher chance to win since no one can exert a higher effort than the bid cap thus the weak players exert more effort than they would in a contest without a bid cap however relatively strong players players with high abilities or high values of winning usually exert higher efforts than the level of the bid cap thus the strong players exert less effort than they would in a contest without a bid cap hence the effect of the bid cap on the players total effort depends on the trade off between the increase of the weaker players efforts and the decrease of the stronger players efforts to be fully effective the bid cap system must guarantee that as many players as possible raise their efforts to the level of the bid cap and as less as possible reduce their efforts to this level

performance responses to competition across skill levels in rank order tournaments field evidence and implications for tournament design tournaments are widely used in the economy to organize production and innovation we study individual data on 2775 contestants in 755 software algorithm development contests with random assignment the performance response to added contestants varies nonmonotonically across contestants of different abilities precisely conforming to theoretical predictions most participants respond negatively whereas the highest skilled contestants respond positively in counterfactual simulations we interpret a number of tournament design policies number of competitors prize allocation and structure number of divisions open entry and assess their effectiveness in shaping optimal tournament outcomes for a designer

the generalized war of attrition abstract we model a war of attrition with n k firms competing for n prizes in a natural oligopoly context the k 1 lowest value firms drop out instantaneously even though each firm s value is private information to itself in a standard setting context in which every competitor suffers losses until a standard is chosen even after giving up on its own preferred alternative each firm s exit time is independent both of k and of other players actions our results explain how long it takes to form a winning coalition in politics solving the model is facilitated by the revenue equivalence theorem jel d43 d44 l13 o30

patent protection and r d with endogenous market structure in a model with endogenous number of innovating firms we show that whether patent protection increases r d investment is ambiguous and depends on the market demand function and the cost of r d if the market size increases with number of firms patent protection reduces r d investment if the cost of r d is sufficiently high and higher product differentiation increases the possibility of lower r d investment under patent protection if the market size does not increase with number of firms patent protection never reduces r d investment we find that welfare is lower under patent protection than under no patent protection

favoring the winner or loser in repeated contests should a firm favor a weaker or stronger employee in a contest despite a widespread emphasis on rewarding the best employees managers continue to tolerate and even favor poor performers contest theory reveals that evenly matched contests are the most intense which implies that a contest designer can maximize each player s effort by artificially boosting the underdog s chances we apply this type of handicapping to a two period repeated contest between employees in which the only information available about their abilities is their performance in the first period in this setting employees are strategic and forward looking such that they fully anticipate the potential impact of the first period contest result on the second period contest and thus adjust their behaviors accordingly the manager also incorporates these strategic behaviors of employees when determining an optimal handicapping policy if employees abilities are sufficiently different favoring the first period loser in the second period increases the total effort over both periods however if abilities are sufficiently similar we find the opposite result occurs total effort increases the most in response to a handicapping strategy of favoring the first period winner

auctions versus negotiations which is the more profitable way to sell a company an auction with no reserve price or an optimally structured negotiation with one less bidder we show under reasonable assumptions that the auction is always preferable when bidders signals are independent for affiliated signals the result holds under certain restrictions on the seller s choice of negotiating mechanism the result suggests that the value of negotiating skill is small relative to the value of additional competition the paper also shows how the analogies between monopoly theory and auction theory can help derive new results in auction theory jel d44 g34 there are close analogies between standard price theory and the theory of auctions in an absolute english auction in which the price rises continuously until only one bidder remains and the seller is required to accept the final bid the sale price equals the lowest competitive price at which supply equals demand in the theory of optimal auctions the seller is treated as a monopolist who can choose any

the tradeoff between performance and quitting in high power tournaments tournaments may be characterized by the performance they induce as well as by the rate of quitting and dropouts of participants although most of the attention in the literature is on the performance induced by high power incentives there are many daily situations in which dropouts and quitting are a major concern using a field experiment in schools and a model of dynamic tournament we examine the effect of different levels of rewards on the rate of quitting our experiment indicates that there is a possible tradeoff between performance and quitting strong incentives tournaments induced participants to exert more effort and exhibit a better performance but at the same time it induces a higher rate of quitting we present a multi stage tournament model that gives rise to a similar characterization jel c93 c73 d8 j30

collective versus individual sale of television rights in league sports in many countries the collective sale of tv rights by sports leagues has been challenged by the antitrust authorities in several cases however leagues won in court on the ground that sport cannot be considered a standard good in this paper we investigate the conditions under which the sale of tv rights collectively by sports leagues rather than individually by teams is preferred from a social welfare viewpoint we find that collective sale is socially preferable when leagues are small relatively homogeneous in terms of clout and where teams get little performance related revenues

an analysis of the war of attrition and the all pay auction we study the war of attrition and the all pay auction when players signals are affiliated and symmetrically distributed we a find sufficient conditions for the existence of symmetric monotonic equilibrium bidding strategies and b examine the performance of these auction forms in terms of the expected revenue accruing to the seller under our conditions the war of attrition raises greater expected revenue than all other known sealed bid auction forms journal of economic literature classification numbers d44 d82 1997 academic press

all pay auctions with certain and uncertain prizes abstract we study all pay auctions with multiple prizes the players have the same value for all the certain prizes except for one uncertain prize for which each player has a private value we characterize the equilibrium strategy and show that independent of the ranking of the uncertain prize if the uncertain prize is not the lowest one a player s effort as well as his expected payoff increase in his value for the uncertain prize otherwise if this prize is the lowest one we obtain that a player s effort may decrease in his value for the uncertain prize but his expected utility increases

optimal prize allocation in contests the role of negative prizes abstract in this paper we analyze the role of negative prizes in contest design with a fixed budget risk neutral contestants and independent private abilities the effort maximizing prize allocation rule features a threshold when the highest effort is above the threshold all contestants with lower efforts receive negative prizes these negative prizes are used to augment the prize to the contestant with the highest effort which better incentivizes contestants with higher abilities when no contestant s effort exceeds the threshold all contestants equally split the initial budget or a portion of it to ensure their participation we find that allowing negative prizes can increase the expected total effort dramatically in particular if no bound is imposed on negative prizes the expected total effort can be arbitrarily close to the highest possible effort inducible when all contestants have the maximum ability with certainty the above contest is shown to be the optimal mechanism for a more general class of mechanisms