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

tullock contests may be revenue superior to auctions in a symmetric setting we consider a symmetric two player common value setting where each player gets a private signal about the object value we show that for some parameter values the equilibrium revenue can be higher in a tullock contest than in the standard auctions

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

caps on political lobbying the cost of political campaigns in the u s has risen substantially in recent years for example real spending on congressional election campaigns doubled between 1976 and 1992 steven d levitt 1995 there are many reasons why increased campaign spending might be socially harmful first increased spending means increased fund raising which may keep politicians from their legislative duties 1 second a lobbyist who makes a large campaign contribution may have undue influence on electoral outcomes on the shaping of legislation or on the outcome of regulatory proceedings 2 that is the socially preferred candidate or legislation may not prevail likewise a lobbyist involved in a regulatory matter or a competition for a government contract may benefit unduly from a legislator s intervention 3 third a perception that campaign contributions purchase influence may lead to increased tolerance of corruption in the private sector a desire to control campaign spending has spawned many initiatives to limit both campaign contributions and spending beginning with the passage of the federal election campaign act feca political action committees pacs can contribute at most 5 000 per election to a candidate while individuals can contribute at most 1 000 restrictions have also been put on in kind contributions making it more difficult to circumvent these limits 4 while direct restrictions on campaign spending have proven difficult to implement recent initiatives aim to impose voluntary spending limits and stricter limits on contributions 5 despite the existing legislation and the proposals to limit contributions little is known about the impact of contribution limits on aggregate expenditures while it is intuitively appealing that aggregate expenditures would drop we challenge that intuition here we study a lobbying game and show that a cap on individual lobbyists expenditures may have the perverse effect of increasing aggregate expenditures and loweri this abstract was borrowed from another version of this item

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

uncertainty polarization and proposal incentives under quadratic voting we consider the quadratic voting mechanism lalley and weyl in quadratic voting working paper university of chicago 2015 weyl in the robustness of quadratic voting working paper university of chicago 2015 and focus on the incentives it provides individuals deciding what proposals or candidates to put up for a vote the incentive compatibility of quadratic voting rests upon the assumption that individuals value the money used to buy votes while the budget balance efficiency of the mechanism requires that the money spent by one voter by redistributed among the other voters from these assumptions we show that it follows that strategic proposers will have an incentive to offer proposals with greater uncertainty about individual values similarly we show that in an electoral setting quadratic voting provides an incentive to propose candidates with polarized non convergent platforms

contests with small noise and the robustness of the all pay auction this paper considers all pay contests in which the relationship between bids and allocations reflects a small amount of noise prior work had focused on one particular equilibrium however there may be other equilibria to address this issue we introduce a new and intuitive measure for the proximity to the all pay auction this allows in particular to provide simple conditions under which actually any equilibrium of the contest is both payoff equivalent and revenue equivalent to the unique equilibrium of the corresponding all pay auction the results are shown to have powerful implications for monopoly licensing political lobbying electoral competition optimally biased contests the empirical analysis of rent seeking and dynamic contests

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

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

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

should lotteries offer discounts on multiple tickets in a complete information setting we show that the standard lottery in which each lottery ticket is offered for the same price is an optimal fundraising mechanism in the presence of strong asymmetries in the way bettors value the prize and the public good provided with the lottery proceeds when participants are more homogeneous it is optimal to offer discounts for the purchase of multiple tickets

disclosure policy in tullock contests with asymmetric stochastic entry we examine how disclosure policy can be optimally designed to incentivize contestants when their participation is exogenously stochastic in a generalized tullock contest setting with two players who are asymmetric in both their values and entry probabilities we fully characterize the necessary and sufficient conditions under which no disclosure dominates full disclosure we find that the comparison depends solely on a balance effect exercised by entry probabilities on the expected total effort the optimal disclosure policy must better balance the competition these conditions continue to hold when the precision r of tullock contests is endogenously chosen by the designer

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

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

gordon tullock entrepreneur of public choice when gordon tullock first encountered james m buchanan in 1957 as an initial step in his transition from the bureaucracy of the u s department of state to the ivy league atmosphere of the university of virginia he carried with him a voluminous manuscript on bureaucracy that he had tried unsuccessfully to publish buchanan 1987a 11 although eight years would pass before that manuscript eventually would be published three years after publication of the calculus of consent 1962 tullock s pioneering instincts already had directed him to the as yet uncharted path of public choice already had alerted him to the ubiquitous presence of homo economicus in the marketplace of politics buchanan quickly recognized the potential importance of combining tullock s insight with his own wicksellian notion of the importance of consent in political process as the basis for a radical research program trespassing across the traditional boundaries of economics and politics ignoring tullock s lack of formal training in economics buchanan installed him in the thomas jefferson center for studies in political economy and thereby provided that crucially important initial support absent which many a potential entrepreneur has failed to fulfill his talent steadfast in this judgment and firm in his resolve buchanan later was to gamble his own career together with the future of the virginia school of political economy in a 1968 exodus from charlottesville as the left leaning ideologically activist bureaucracy of thomas jefferson s academy thrice denied tullock a well earned promotion to full professor breit 1986 buchanan s judgment was sound and the virginia school reemerged unscathed and fortified as buchanan and his protege regrouped in the foothills of the appalachian mountains to carry the baton of the virginia public choice research

when less is more rationing and rent dissipation in stochastic contests this paper shows how to maximize revenue when a contest is noisy we consider a case where two or more contestants bid for a prize in a stochastic contest where all bidders value the prize equally we show that whenever a tullock contest yields under dissipation the auctioneer s revenue can be increased by optimally fixing the number of tickets in particular in a stochastic contest with proportional probabilities it is possible to obtain almost full rent dissipation we test this hypothesis with a laboratory experiment the results indicate that as predicted revenue is significantly higher in a lottery with rationing than in a standard lottery on the other hand an alternative rationing mechanism that does not limit total expenditures fails to increase revenue relative to a standard lottery

the effect of private interests on regulated retail and wholesale prices abstract this paper examines how regulators behave in markets when there is a tension between retail competition and cross subsidy using retail and wholesale prices from regional bell operating company territories and price cost margins as a proxy for political influence we find that private interests influence the structure of retail prices especially favoring rural residential customers political influence also extends to wholesale access prices although the magnitude of its effect is small federal high cost universal service payments to a state do not reduce prices in that state s rural areas but instead lower urban business prices

rent dissipation when rent seekers are budget constrained in the original tullock 1975 1980 game an individual bidder s probability of winning with a bid b is proportional to br where the exponent reflects economies of scale in rent seeking different interpretations can be given to these probabilities first one may view r as a reflection of the political culture alternatively one may view r as a choice variable for a politician intuition suggests that a society with a high tolerance for the selling of political favors and politicians who are receptive to rent seeking would both induce greater rent seeking expenditures than other societies all else equal this paper shows that a lower value of r can actually lead to more rent dissipation than a higher value this paper also reinforces two points concerning rent seeking first the analysis confirms the robustness of under dissipation of rents even in the face of entry second it points out the importance of distinguishing between rent seeking expenditures and rent dissipation when bidders must borrow for example total expenditure may understate rent dissipation

the economic future of europe after three years of near stagnation the mood in europe is definitely gloomy many doubt that the european model has a future in this paper i argue that things are not so bad and there is room for optimism over the last thirty years productivity growth has been much faster in europe than in the united states productivity levels are roughly similar today in the european union and in the united states the main difference is that europe has used some of the increase in productivity to increase leisure rather than income while the united states has done the opposite still not everything is well unemployment is still high and europe suffers from inefficient regulation here also however there is more action than often perceived and a wide ranging reform process is taking place this process is driven by reforms in financial and product markets reforms in those markets are in turn putting pressure for reform in the labor market reform in the labor market is slowly taking place but not without political tensions these tensions dominate the news but they are a symptom of change not a reflection of immobility

how lotteries outperform auctions in their recent paper goeree et al 2005 determine that all pay auctions are better for fundraising activities than lotteries we show that the introduction of asymmetry among participants with complete information could reverse this result complete information seems well suited to some charity environments

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

rent seeking with asymmetric valuations this paper analyzes tullock s rent seeking game with asymmetric valuations for a variable range of the returns to scale parameter a necessary and sufficient condition for a unique pure strategy nash equilibrium is established equilibrium effort and expected profits are determined and subjected to comparative statics analysis increasing the underdog s valuation induces both players to increase their efforts increasing the favorite s valuation increases his effort but decreases the effort of the underdog expected profits increase with a player s valuation but decreases with the valuation of the competitor the impact of the returns to scale parameter is also analyzed

incentives in lottery contests with draws abstract we investigate the incentive consequences of introducing the possibility of draws into lottery contests equilibrium total effort unambiguously decreases when draws are introduced whereas the equilibrium expected winner s effort increases when the contestants valuations of the prize become sufficiently dispersed