the solution to the tullock rent seeking game when r 2 mixed strategy equilibria and mean dissipation rates in tullock s rent seeking model the probability a player wins the game depends on expenditures raised to the power r we show that a symmetric mixed strategy nash equilibrium exists when r 2 and that overdissipation of rents does not arise in any nash equilibrium we derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete and show that full rent dissipation occurs when the strategy space is continuous our results are shown to be consistent with recent experimental evidence on the dissipation of rents

semi targeted all pay auctions a partial exclusion principle abstract this paper studies the effects of a specific affirmative action policy in complete information all pay auctions when players differ in ability the contest organizer splits the overall prize of the competition into a targeted and an untargeted prize the targeted prize is exclusively for disadvantaged low ability agents and excludes advantaged agents partially from the overall prize we consider a setting with one high ability and two low ability contestants and fully characterize equilibrium assuming that the contest organizer aims to maximize expected total effort we show that i almost any targeted prize is preferable to a standard all pay auction without targeted prize ii the exclusion principle baye et al 1993 can be implemented by a wide range of sufficiently large targeted prizes and iii partial exclusion by means of an appropriately chosen targeted prize benefits the organizer more than complete exclusion we also discuss the robustness of our results in settings with more than three agents

incomplete information and rent dissipation in deterministic contests abstract in a deterministic contest or all pay auction all rents are dissipated when information is complete and contestants are identical as one contestant becomes stronger that is values the prize more total expenditures are known to decrease monotonically thus asymmetry among contestants reduces competition and rent dissipation recently this result has been shown to hold for other non deterministic contest success functions as well thereby suggesting a certain robustness in this paper however the complete information assumption is shown to be crucial i examine a tractable incomplete information model for which the complete information model is a special case with incomplete information regardless of how little total expenditures in a deterministic two player contest increase when one contestant becomes marginally stronger starting from a symmetric contest in fact both contestants expend resources more aggressively with complete information neither of them do so thus there is a discontinuity in the information structure

rent seeking and rent dissipation a neutrality result abstract we consider rent seeking contests between at least two agents who might value the prize differently we capture a wide range of institutional aspects of contests by analyzing a class of contest success functions fulfilling several properties the main properties are anonymity and a condition on the elasticity of a rent seeker s win probability with respect to her effort we show the existence of a mixed strategy equilibrium and establish equilibrium payoffs in this equilibrium complete rent dissipation holds our results imply a partial robustness result for the all pay auction

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

heterogeneous risk loss aversion in complete information all pay auctions we extend previous theoretical work on n player complete information all pay auctions to incorporate heterogeneous risk and loss averse utility functions we provide sufficient and necessary conditions for the existence of equilibria with a given set of active players with any strictly increasing utility functions and characterize the players equilibrium mixed strategies assuming that players can be ordered by their risk aversion player a is more risk averse than player b if whenever player b prefers a certain payment over a given lottery so does player a we find that in equilibrium the more risk averse players either bid higher than the less risk averse players and win with higher ex ante probability or they drop out furthermore while each player s expected bid decreases with the other players risk aversion her expected bid increases with her own risk aversion thus increasing a player s risk aversion creates two opposing effects on total expected bid a sufficient condition for the total expected bid to decrease with a player s risk aversion is that this player is relatively more risk averse compared to the rest of the players our findings have important implications for the literature on gender differences in competitiveness and for gender diversity in firms that use personnel contests for promotions

incentives and careers in academia theory and empirical analysis we study career concerns in italian academia we mould our empirical analysis on the standard model of contests formalised in the multi unit all pay auction the number of posts the number of app

monotone comparative statics in games with non monotonic best replies contests and cournot oligopoly abstract in this paper we employ lattice theoretic techniques to derive a number of comparative statics in a logit contest a class of games for which best replies are generically non monotonic using the same approach we obtain several comparative statics in a cournot oligopoly model without imposing the usual assumptions that ensure the game is one of strategic substitutes our analysis illustrates how lattice theoretic techniques can deliver powerful insights in games with non monotonic best replies

asymmetric contests with conditional investments rent seeking scenarios competitions for promotions and research and development r d races are examples of competitions in which participants expend resources regardless of whether they win or lose although similar in their all pay feature such competitions often differ in important dimensions these include the type of technologies employed in competition the type of asymmetries among competitors the degree to which expenditures are sunk and the number of prizes consider lobbying settings in which firms expend resources in order to influence a policymaker if expenditures take the form of monetary outlays and all firms have the same cost of capital then it is reasonable to think of firms marginal cost of influence as linear but if a firm has a reputational advantage and high costs of capital its lobbying technology may be more reasonably thought of as having convex costs relatively low marginal costs up to a moderate level of influence due to the reputational advantage and relatively high marginal costs at higher levels of influence due to the high costs of capital similarly the lobbying technology of a firm that is relatively unknown and has low costs of capital may be characterized by concave costs lobbying restrictions geographic location or preferential treatment by the policymaker further impact firms lobbying technologies inducing additional nonlinearities and asymmetries among firms in some lobbying settings firms also commit to expenditures conditional on a favorable outcome for example a firm may commit to building factories and creating new jobs if it is granted one of a limited number of manufacturing licenses thus the specification of firms lobbying technologies the type of asymmetries among firms the combination of unconditional and conditional investments and the number of eventual winners may change according to the lobbying setting studied the same is true for other competitions with an all pay feature in a competition for promotions workers often differ in their abilities experience and social skills more than one prize

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

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

a game theoretic model for mergers and acquisitions abstract the corporate merger process is modelled as a bargaining game under certainty the distribution of gains between target and acquiring companies that would be consistent with the nash kalai axioms is determined in principle an operational version of the resulting game theoretic model is fitted to empirical results from 24 recent mergers of companies quoted on the johannesburg stock exchange the model is shown to have good predictive power within this set of data

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 all pay auction with nonmonotonic payoff i model innovation contests as an all pay auction in which it is possible not to achieve successful innovation despite costly r d investments and as a result there is no winner in such a case the winning payoff turns out to be nonmonotonic in own bid i derive the sufficient conditions for the existence of pure strategy equilibria and fully characterize the nondegenerate mixed strategy equilibrium in the mixed strategy equilibrium the support of the low value bidder is not continuous and both the high value and the low value bidders place an atom in the distinct lower bound of their respective support under symmetric valuation both bidders place an atom at zero these results can explain why one does not observe very low quality innovation in real life or why even symmetric firms may stay out of an innovation contest

sequential location games we study location games where market entry is costly and occurs sequentially and where consumers are nonuniformly distributed over the unit interval we show that for certain classes of densities including monotone and under some additional restrictions hump shaped and u shaped ones equilibrium locations can be determined independently of when they are occupied our analysis reveals a number of peculiarities of the uniform distribution extensions of the model allow for price competition and advertisement in media markets winner take all competition trade offs between profits in the short and the long run and firms operating multiple outlets

auctions an introduction abstract this is a detailed introduction to auction theory it begins with a simple analysis of standard auctions and then uses a strikingly simple general solution of symmetric private values auctions to prove the payoff equivalence of many auction rules the basic framework is then modified to admit risk aversion multi unit and repeated auctions as well as collusion then follows an introduction to optimal auctions with and without stochastic entry and to common value auctions and the winner s curse problem the survey closes with a sample of applications from the regulation of natural monopolies to price competition in oligopoly and the government securities market

contest with pre contest investment abstract in a standard noisy contest more competition more contestants leads to lower individual equilibrium effort we show that when contestants can make pre contest investment to enhance their competency neither equilibrium investment nor individual effort is monotonic in the number of contestants individual effort may increase with the level of participation

incorporating policymaker costs and political competition into rent seeking games 1 introductionrent seeking in politics involves agents who lobby policymakers for potential benefits in a seminal contribution tullock 1980 modeled rent seeking as a lottery game a major weakness of tullock s game was that it lacked verisimilitude to actual rent seeking because it omitted politics the absence of politics meant that the game essentially assumed that there are no costs to the policymakers of supplying rents but as tollison 1997 and others have pointed out these costs are not zero and the politics surrounding the policy decision influence the pattern of lobbying and the rent seeking outcome in this paper we address two aspects of those politics the costs to policymakers of supplying rents and the variable intensity of political competition among a given number of rent seekers including these aspects increases the similarity of the game to actual rent seeking situations and makes clearer the incentives to rent seekers costs to supplying rents arise due to various constraints legislators must build coalitions acquire parliamentary rights maintain a positive image and service constituent interests policymakers in agencies must follow procedural rules submit to congressional oversight and budgeting pass omb reviews and so forth lower policymaker costs should increase the effectiveness of lobbying and this should attract greater lobbying efforts among rent seekers 1 increasing policymaker costs makes lobbying less effective indeed because of these costs policymakers often turn away lobbies empty handed in short policymakers have constraints that affect the policies they design and this affects lobbying expenditures dougan and snyder 1993 this paper introduces policymaker costs in monetary units such that they are comparable to the value of the rent and rent seeking expenditures political competition among rent seekers also influences the rent seeking outcome competition traditionally has been modeled by varying the number of rent seeking agents actual or potential or their relative lobbying expenditures e g posner 1975 rogerson 1982 sun and ng 1999 competition can vary however even among a given number of rent seekers and for a given profile of expenditures for example two agents may lobby a policymaker for the same unique and exclusive political good then one agent directly opposes the other and only one agent can win the good alternatively the same two agents may lobby a policymaker for two separate political goods in that case the agents oppose each other only indirectly this situation is frequent in politics as rent seeking agents compete for space on the political agenda for policymakers time and for portions of a particular government budget in this situation success by one agent does not necessarily result in failure by the other but it does lower the probability that the other agent will succeed competition is more intense in the first example even though the examples involve the same number of firms industrial organization economists have shown that a single parameter can determine incumbent firms competition in price and quantity regardless of the number of firms present 2 this paper introduces rent seeking competition analogously allowing a parameter to alter the competitiveness of the rent seeking game among a fixed number of firms we incorporate monetized policymaker costs and the political competition parameter into the success probabilities of the standard rent seeking game the resulting model is a game in which the agents simultaneous maximization of expected net returns or profits determines a nash equilibrium in their expenditures incorporating politics into the standard game makes the game more accurate because equilibrium and comparative statics depend in part on the politics of the rent seeking contest more specifically increasing political competition decreases rent seeking expenditures unless the value of the rent is sufficiently large relative to policymaker costs and dissipation rates are lower than in previous research because of policymaker costs

contest functions theoretical foundations and issues in estimation contest functions alternatively contest success functions determine probabilities of winning and losing as a function of contestants e ort they are used widely in many areas of economics that employ contest games from tournaments and rent seeking to conflict and sports we first examine the theoretical foundations of contest functions and classify them into four types of derivation stochastic axiomatic optimally derived and microfounded the additive form which includes the ratio or tullock functional form can be derived in all four di erent ways we also explore issues in the econometric estimation of contest functions including concerns with data endogeneity and model comparison

expected revenue of all pay auctions and first price sealed bid auctions with budget constraints we show that all pay auctions dominate first price sealed bid auctions when bidders face budget constraints this ranking is explained by the fact that budget constraints bind less frequently in the all pay auctions which leads to more aggressive bidding in that format

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

policy influence and private returns from lobbying in the energy sector in this article i quantify the extent to which lobbying expenditures by firms affect policy enactment to achieve this end i construct a novel dataset containing all federal energy legislation and lobbying activities by the energy sector during the 110th congress i then develop and estimate a game theoretic model where heterogeneous players choose lobbying expenditures to affect the probability that a policy is enacted i find that the effect of lobbying expenditures on a policy s equilibrium enactment probability to be statistically significant but very small nonetheless the average returns from lobbying expenditures are estimated to be over 130

the exclusion principle for symmetric multi prize all pay auctions with endogenous valuations abstract this paper explains why contest designers may limit entry into a symmetric multi prize all pay auction the revenue maximizing size of the group of finalists depends on the extent to which prize values decrease or increase with the number of contestants

optimal favoritism in all pay auctions and lottery contests abstract we analyze the revenue enhancing potential of favoring specific contestants in complete information all pay auctions and lottery contests with several heterogeneous contestants two instruments of favoritism are considered head starts that are added to the bids of specific contestants and multiplicative biases that give idiosyncratic weights to the bids in the all pay auction head starts are more effective than biases while optimally combining both instruments even yields first best revenue in the lottery contest head starts are less effective than biases and combining both instruments cannot further increase revenue as all pay auctions revenue dominate lottery contests under optimal biases we thus obtain an unambiguous revenue ranking of all six combinations of contest formats and instruments

analysis of preference dependencies among objectives in decision problems there are often preference dependencies for the achievement of various objectives this paper suggests a problem oriented approach to address such preference dependencies first a diagnostic analysis is conducted to identify the basis for the dependencies based on this the attributes are divided into components or transformed into an alternate set of attributes with a lesser degree of preference dependence quantification of the value structure by developing a utility function is easier in such cases making use of existing independence concepts

the all pay auction when a committee awards the prize there is very little work on the equilibrium of the all payauction when the prize is awarded by two or more people iconsider an all pay auction under committee administrationwith caps on the bids of the contestants i show that for anynumber of committee members and contestants there exists apure strategy equilibrium in which the contestants bid anamount equal to a suitably chosen cap i argue that the cap isnot an artificial restriction on the game given that thereare caps on political lobbying in the real world i find thatcommittee administration could result in higher aggregateexpenditures even if there is some probability that thecommittee will not award the prize the intuition for thisresult is that the inclusion of additional administratorsrelaxes the effect of caps on lobbying that is caps onlobbying tend to be more effective the smaller is the size ofthe committee caps may also be a solution to the problem ofmajoritarian cycles in all pay auctions under committeeadministration

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

difference form contests and the robustness of all pay auctions abstract in much of the existing literature on rent seeking games the outcome of the contest is either infinitely sensitive or relatively insensitive to contestants efforts the current paper presents a family of contest games that permit characterization of equilibrium for all levels of sensitivity of the outcome to contestants efforts specifically the outcome of the contest depends on the difference between efforts which encompass the lottery and the all pay auction as polar cases the equilibrium converges to that of the all pay auction as the probability of winning the prize grows infinitely sensitive to one s effort and the main qualitative features of equilibrium persist over a large parameter region journal of economic literature classification numbers d44 d72

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

elections with platform and valence competition abstract we study a game in which candidates first choose platforms and then invest in costly valences e g engage in campaign spending the marginal return to valence depends on platform polarization the closer platforms are the more valence affects the election outcome consequently candidates without policy preferences choose divergent platforms to soften valence competition moreover exogenous increases in incentives for valence accumulation lead to both increased valence and increased polarization the latter because candidates seek to avoid the costs of extra valence as a result the increase in valence is smaller than it would have been with exogenous platforms finally the model highlights the overlooked substantive importance of common modeling assumptions changing the source of uncertainty in our model from noise around the median voter s ideal point to a shock to one candidate s valence as is common in the literature leads to complete platform convergence for all parameter values

on the evolution of prize perceptions in contests abstract we apply an indirect evolutionary approach to players perceived prize valuations in contests evolution in finite populations leads to preferences that overstate the prize s material value and induce overexpenditure we establish an equivalence between evolutionarily stable strategies and the behavior induced by evolutionarily stable preferences

entry into winner take all and proportional prize contests an experimental study this experiment compares the performance of two contest designs a standard winner take all tournament with a single fixed prize and a novel proportional payment design in which that same prize is divided among contestants by their share of total achievement we find that proportional prizes elicit more entry and more total achievement than the winner take all tournament the proportional prize contest performs better by limiting the degree to which heterogeneity among contestants discourages weaker entrants without altering the performance of stronger entrants these findings could inform the design of contests for technological and other improvements which are widely used by governments and philanthropic donors to elicit more effort on targeted economic and technological development activities

carrots and sticks prizes and punishments in contests i introduction contests are widely used to model political lobbying sports competitions job promotions and r d races in most cases the contest s organizer has some control over the structure of rewards and punishments teachers determine who passes and who fails the exam a company sets rules about promotions and layoffs and sport governing bodies choose the number of teams advancing to a higher league and the number of those relegated to a lower one in this paper we characterize the optimal prize structure in a contest where the designer can use both rewards carrots and punishments sticks in order to motivate participants to exert effort 1 although both rewards and punishments are part of many existing incentive contracts the literature on contests focused on the incentive role of rewards because a contest that uses some punishments can be replicated by one that uses only rewards and yields the same incentives but this equivalence breaks down if the contest designer faces a budget constraint and if both rewards and punishments are costly the main focus of the present paper is to study contest design when the designer is budget constrained and it is costly to punish or reward players costly punishments appear in many situations for example in labor tournaments a firm usually incurs costs when firing workers who perform poorly e g worker compensation production disruption loss of clients and usually face search and replacement costs e g think about a faculty denying tenure to some candidates in other instances punishments are less costly to implement e g relegation in sport tournaments and we also briefly deal with this set up we assume here that the designer has a limited budget which means that costly punishments cannot be arbitrarily high subject to her budget constraint the designer determines the number and size of prizes punishments in order to maximize the participants expected total effort in particular some prizes can be positive rewards or negative punishments given the prize structure players choose their effort levels in order to maximize their expected payoff it is important to note that in a contest with n participants the marginal effect of each of n prizes on the participants total effort is different and can be either positive or negative if the marginal effect of the k th prize is positive its value given a budget constraint should be positive reward or zero and if the marginal effect is negative its value should be negative punishment or zero thus given that the contest designer has a limited budget he will prefer to distribute the entire prize sum to the prize with the highest marginal effect on the participants total effort relative to its cost in this paper we show that the relative effectiveness of punishments compared to rewards crucially depends on the curvature of the distribution of player abilities exploiting results about normalized spacings among order statistics developed by barlow and prochan 1966 we first revisit one of the main results in moldovanu and sela 2001 if punishment is not feasible the optimal prize structure offers a single reward to the top performer if rewards are not feasible we then show that the designer should only punish the player with the lowest performance if the distribution of abilities has an increasing hazard or failure rate if this last condition is not satisfied more punishments may be optimal if the designer can punish as well as reward the optimal prize structure will depend on the relative marginal cost of punishments and on the distribution of the players abilities for example if the marginal cost of punishments is the same as the marginal cost of rewards it is optimal to punish the worst performing player if the distribution of abilities is convex if that player is punished even high types will work hard to avoid performing worst because they know that there is a relatively high probability that competitors also have high types

a comparative evaluation of multiattribute consumer preference models in this paper the theory and estimation procedures for several consumer preference models are discussed predictive accuracy in the form of internal consistency of these models is compared in an empirical application consumer decision situations are classified into two classes decisions under certainty and decisions under uncertainty for each of the two classes of decision situations two modeling strategies have been used statistical estimation and algebraic solution an additive conjoint an additive and a multiplicative measurable value and an additive and a multiplicative utility model are considered our main finding is that the statistical estimation procedures outperform their algebraic counterparts on the criterion of predictive accuracy the utility model provides better predictions for decisions under uncertainty than the widely used conjoint models the relationship between models for decisions under certainty and decisions under uncertainty is discussed it is shown how a conjoint or a mea

rigging the lobbying process an application of the all pay auction textabstractin a world where a politician can explicitly auction off a prize to the high bidder the standard auction literature can be used to analyse political behavior the justice system however precludes politicians from explicitly selling the prize to the highest bidder thus politicians cannot let it become public knowledge that they are in the business of selling political favors an institution has emerged in political markets to overcome this constraint which are termed as lobbying lobbyists make implicit payments to the politician through campaign contributions if these up front payments were rebated to those failing to receive the prize it would be clear that the politician was selling favors this article has examined an interesting principle arising in all pay auctions this principle states that a politician wishing to maximize political rents may find it in his best interest to exclude certain lobbyists from participating in the lobbying process particularly lobbyists valuing most the political prize

import prices export prices and the current account an asymmetry abstract we demonstrate that there is an important asymmetry between the effects of temporary import and export price shocks on the current account that is ignored in theoretical and empirical work this asymmetry is found to hold for u s and u k data

early round upsets and championship blowouts i introduction popular discussions of tournament play often celebrate the success of underdogs in early rounds and decry the prevalence of unexciting finals such a pattern might be just a statistical illusion there are many early round matches so some upsets are inevitable and there is only one final so it is unlikely to be the most exciting match of the tournament in this article we consider instead whether the pattern might have a real foundation in the strategic allocation of effort by tournament participants we analyze a two round tournament in which a favorite and underdog play in each of the two semifinals and then one player from each match advances to the final victory in a match is probabilistic in that the chance of winning is increasing in each player s relative quality and in his relative effort expenditure 1 each player has a fixed amount of effort to exert over the two rounds unused effort is of no value and the only payoff is from winning the tournament to maximize the chance of winning each player must balance out the benefits of expending more effort in the semifinal against the opportunity cost of having less effort available for the final favorites and underdogs both have an incentive to conserve resources for the final but the trade offs they face are different a favorite plays a weak opponent in the semifinal but is likely to face a tough opponent in the final so it has a strong incentive to hold back conversely an underdog already plays a tough opponent in the semifinal so it has less incentive to conserve effort for the final 2 because of these different incentives we find that in any symmetric nash equilibrium underdogs exert more effort than favorites do in the semifinal the extra effort does not fully compensate for lower ability and underdogs are still likely to lose but the chance of an upset rises in the final round each player expends all its remaining resources so differences in abilities are no longer compressed by strategic considerations instead an underdog who makes it to the final has fewer resources left to spend than the favorite so differences in abilities are amplified and the chance of a blowout by the favorite rises if a favorite loses to an underdog in the early rounds it is often accused of looking past the underdog to its next match even if a player s strategy is optimal ex ante it might turn out to be unsuccessful ex post so such criticism is often unfair our results imply that it is rational for the favorite to hold back on resources in the semifinal even if it correctly anticipates that in equilibrium the underdog will be playing harder sometimes the strategy will backfire but on average the favorite benefits from being in a better position for the final these results are derived using a standard contest model in which each player s probability of victory in a match is a strictly increasing function of his ability and effort 3 such models were first developed to analyze rent seeking tullock 1967 1980 and similar models appear in a wide variety of areas including patent races loury 1979 election campaigns snyder 1989 compensation schemes nalebuff and stiglitz 1983 career ladders lazear and rosen 1981 lobbying baye et al 1993 and sports contests szymanski 2003 4 more specifically we model the contest as a sequential elimination ladder tournament in which players first compete in separate groups and the winners then compete against each other rosen 1986 our result that underdogs do indeed try harder than favorites in the semifinals contrasts with that of rosen 1986 p 707 8 because the favorite has a better chance of victory in the final rosen finds that winning a semifinal match is more valuable to the favorite so the favorite tries harder than the underdog we reach the opposite conclusion because we assume that there is a fixed supply of effort to be used across rounds and unused effort in the tournament has no value

decision by sortition a means to reduce rent seeking this essay gives an overview of how arandomized decision mechanism sortition can be expected to reduce the intensity ofself interested activity by rent seekingfactions within democracies the socialcosts of rent seeking are briefly reviewed i then make the case that randomization ofcollective decision making proceduresattenuates rent seeking expenditures iillustrate the argument by reference to thehighly contested presidential election of2000 finally i buttress that argument bycomparing plurality voting and sortitionwithin the context of tullock s efficient rent seeking model 1980

all pay auctions with a buy price option all pay auctions this paper studies all pay auctions in which there is a buy price option for bidders to guarantee purchases at a seller specified price we analyze symmetric increasing bidding equilibria in the first and second price all pay auctions with the buy price option while the optimal buy price in the second price is higher than are those in the first price all pay auction both formats maintain the same expected profit with an endogenous entry process all pay auctions with the buy price can attract more consumers and ultimately reach a higher expected profit than does the uniform posted price selling mechanism jel d44 l11 l81

the existence of equilibrium in discontinuous economic games i theory the article presents information about the existence of equilibrium in discontinuous economic games in this paper and its sequel presents study the existence of nash equilibrium in games where agents payoff functions are discontinuous the enquiry is motivated by a number of recent studies that have uncovered serious existence problems in seemingly innocuous economic games in the sequel to this paper authors have explained the utility function in the economic games referred to earlier are neither continuous nor quasi concave however they demonstrate that the payoff functions in mildly modified versions of these constructs exhibit two weaker forms of continuity which together with the requirement of quasi concavity suffice for the existence of an equilibrium from this one may conclude that at least in the modified versions of these models discontinuities in the payoff functions are not the real source of the problem rather it is the failure of the payoff functions to the quasi concave which is responsible for the non existence of equilibrium these observations bear on the existence of nash equilibrium in pure strategies

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

equilibrium contingent compensation in contests with delegation we consider two player contests in which each player hires a delegate who expends his effort to win a prize on the player s behalf endogenizing delegation contracts we focus on the equilibrium contracts between the players and their delegates we first show that each player s equilibrium contract is a no win no pay contract then we examine the delegates equilibrium compensation spreads effort levels probabilities of winning expected payoffs and the players equilibrium expected payoffs we show that economic rents for the delegates may exist

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

war and conflict in economics theories applications and recent trends we review the main economic models of war and conflict these models vary in details but their implications are qualitatively consistent highlighting key commonalities across a variety of conflict settings recent empirical literature employing both laboratory and field data in many cases confirms the basic implications of conflict theory however this literature also presents important challenges to the way economists traditionally model conflict we finish our review by suggesting ways to address these challenges

orchestrating rent seeking contests contests have different sometimes quite complex organisational structures in particular while most of the existing literature focusses on simultaneous contests multistage contests are also quite frequently encountered this paper seeks to provide a rationale for the latter by endogenising the choice of a contest structure which is made by an organiser of a contest interested in maximising the efforts expended by the contenders

the design of rent seeking competitions committees preliminary and final contests the paper examines the common practice in multi contest rent seeking competitions where finalists are selected based on rent seekers efforts in a preliminary contest we find that for any single contest design rent seeking expenditures could be reduced by introducing a preliminary contest if the marginal returns to rent seeking effort in the preliminary contest is sufficiently low in addition to other reasons the paper argues that this may explain why such multi contest designs are common we argue that rent seeking expenditure in the preliminary stage represents the cost of reducing the number of contestants we also find that the practice of setting a higher quality standard in the final contest than the quality standard in the preliminary contest reduces rent seeking waste we derive an expression for the optimal number of finalists under certain conditions we find that the optimal number of finalists is directly proportional or equal to the square root of the number of potential contestants finally we show that whether rent seeking expenditures rise or fall when the rent is awarded by a committee instead of a single administrator depends on the sensitivity of the committee relative to that of the single administrator

asymmetry and corrective public policy in contests the proposal of an inefficient policyusually stimulates a political strugglebetween the affected interest groups theresulting wasteful lobbying activities mayreduce welfare even if the proposed policyis not approved in this paper weshow that sufficient asymmetry in payoffsnot only tends to reduce lobbying effortsin standard rent seeking contests as iswell known but it is in fact a necessarycondition for the implementation of asuccessful effective correctivetax transfer policy that complements theproposal of the inefficient policy such apolicy induces an efficient equilibriumoutcome which is in addition optimal fromthe viewpoint of the players that take partin the public policy game

externalities in recruiting external recruiting at least weakly improves the quality of the pool of applicants but the incentive implications are less clear using a contest model this paper investigates the pure incentive effects of external recruiting our results show that if workers are heterogeneous opening up a firm s career system may lead to a homogenization of the pool of contestants and thus encourage the firm s high ability workers to exert more effort if this positive effect outweighs the discouragement of low ability workers the firm will benefit from external recruiting if however the discouragement effect dominates the homogenization effect the firm should disregard external recruiting in addition product market competition may mean that opening up the career system becomes less attractive for a firm since it increases the incentives of its competitors workers and hence strengthens the competitors

politician preferences law abiding lobbyists and caps on political contributions the effect of a contribution cap is analyzed in a political lobbying game where the politician has a policy preference in contrast to the previous literature without politician policy preferences more restrictive binding caps always reduce expected aggregate contributions however the initial imposition of a cap increases contributions if the politician mildly favors the low valuation lobbyist s policy the introduction of policy preferences permits analysis of monied interests policy influence a more restrictive cap makes it more likely that the politician enacts the policy he would have enacted in the absence of lobbying even in cases where expected aggregate contributions increase

markets for ideas prize structure entry limits and the design of ideation contests contests are a popular mechanism for the procurement of innovation in marketing design and other creative industries firms use freelance marketplaces to organize contests and obtain high quality ideas for ads new products and even business strategies from participants a central question faced by contest sponsors is how to appropriately structure prizes and entry regulations i develop an empirical model of idea generation ideation contests and investigate the impact of the number of prizes prize amount and submission limit on participation and quality outcomes using data from a popular marketing ideation platform the model explains participant submission decisions jury ratings and sponsor rankings of winning submissions counterfactuals reveal the impact of design parameters on outcomes and provide guidance for the optimal design of ideation contests and platforms

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

contest efforts in light of behavioural considerations this study shows that distortion of probabilities is a possible reason for rent under dissipation incontests with relatively small number of participants such distortion may also result however inover dissipation of the contested rent focusing on contests with homogeneous contestants and thecommonly studied contest success function our main results clarify under what circumstances i rents are more under dissipated relative to the standard situation where probabilities are notdistorted ii rents are under dissipated yet less intensely relative to the standard situation whereprobabilities are not distorted iii rents are over dissipated and iv the contest does not possess asymmetric interior equilibrium in pure strategies

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

a game theoretic analysis of skyscrapers abstract skyscrapers are urbanism in the extreme but they have received surprisingly little direct attention in urban economics the standard urban model emphasizes differentials in access across locations which determine land price differentials and building heights this explanation leaves out an important force that appears to have historically influenced skyscraper construction an inherent value placed on being the tallest in this paper we present a game theoretic model of skyscraper development that captures this additional force the model predicts dissipative competition over the prize of being tallest a prediction consistent with the historical record the paper discusses the implications of this result for the nature and efficiency of urban development and for the operation of urban real estate markets

show them your teeth first a game theoretic analysis of lobbying and presure this paper investigates the choice of an interestgroup between lobbying words and pressure actions in order to influence a policymaker both lobbying and pressure are modeled asstrategic means of transmitting information that isrelevant to the policymaker however only pressure isdirectly costly to the policymaker the interactionbetween the interest group and the policymaker isframed as a repeated signaling game in equilibriumpressure in contrast to lobbying only occurswhen the interest group s reputation is sufficientlylow and always improves its reputation it is shownthat repeated lobbying cannot completely substitutefor pressure and that the interest group may beforced to sustain its reputation through lobbying weconclude that pressure is typically used to build upa reputation lobbying to maintain a reputation

lottery versus all pay auction models of lobbying i first provide a complete characterization of the unique equilibrium of the lottery game by n lobbyists with asymmetric valuations and then compare the lottery and the all pay auction models of lobbying i show that the exclusion principle discovered by baye kovenock and de vries 1993 for all pay auction does not apply to lottery i also show that the perverse effect that an exogenous cap may increase the total lobbying expenditure in a two bidder all pay auction discovered by che and gale 1998 does not apply to lottery

contests with three or more heterogeneous agents abstract we study monotone equilibrium behavior in contests with observable effort bid where three or more participants have distinct risk attitudes and the monetary value for the prize of each is drawn independently from a distinct distribution these differences can either cause a player to drop out that is always choose zero effort regardless of his valuation or use all or nothing strategies with discontinuous effort choice neither complete drop out nor discontinuous bidding with finitely many gaps is consistent with pure strategy monotone bayesian nash equilibrium in a contest with either ex ante identical players or only two distinct participants

the incidence of overdissipation in rent seeking contests tullock s analysis of rent seeking and overdissipation is reconsidered we show that while equilibrium strategies do not permit overdissipation in expectation for particular realizations of players mixed strategies the total amount spent competing for rents can exceed the value of the prize we also show that the cross sectional incidence of overdissipation in the perfectly discriminating contest ranges from 0 50 to 0 44 as the number of players increases from two to infinity thus even though the original analysis of overdissipation is flawed there are instances in which rent seekers spend more than the prize is worth

bidding for a group specific public good prize abstract we examine the equilibrium effort levels of individual players and groups in a contest in which two groups compete with each other to win a group specific public good prize the players choose their effort levels simultaneously and independently and the winning group is determined by the selection rule of all pay auctions we first prove nonexistence of a pure strategy nash equilibrium and then construct a mixed strategy nash equilibrium at the nash equilibrium the only active player in each group is a player whose valuation for the prize is the highest in that group all the other players expend zero effort and the equilibrium effort levels depend solely on two values the highest valuation for the prize in each group

should we tax or cap political contributions a lobbying model with policy favors and access abstract this paper develops a model of political contributions in which a politician can either sell policy favors or sell access access allows interest groups to share hard information with the politician in support of their preferred policy here selling access maximizes policy utility while selling policy favors maximizes total contributions imposing a binding contribution limit makes it more likely that the politician sells access which can improve expected constituent welfare however a contribution limit distorts the signals associated with the contributions which tends to result in worse policy alternatively a tax on political contributions can ensure that the politician sells access without distorting his information therefore from the viewpoint of a representative constituent a tax on contributions is strictly preferred to a contribution limit or no reform the politician however may prefer regulation in the form of a contribution limit even when a tax is better for the constituent

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

soft money and campaign finance reform we analyze special interest influence on policy when political contributions are capped but the regulation contains soft money loopholes the politician chooses between two policy options we define special interest influence as the probability the politician chooses the policy he would not have chosen in the absence of contributions any binding cap reduces special interest influence but the effect may be nonmonotonic a ban on contributions can result in greater special interest influence than a binding but nonzero cap the results may also have implications for the policy response to the 2010 supreme court ruling on citizens united v fec