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

semicollusion in the norwegian cement market abstract a model of semicollusion where firms collude on prices and compete on capacities is tailor made to the characteristics of the norwegian cement market and tested on this particular market for the period 1927 1982 the results indicate that the rapid increase in capacity and thereby in exports in the period 1956 1967 the late phase of the price cartel best can be explained by the market sharing agreement each firm overinvested in capacity to receive a large quota in the domestic market

contracts as a barrier to entry it is shown that an incumbent seller who faces a threat of entry into his or her market will sign long term contracts that prevent the entry of some lower cost producers even though they do not preclude entry completely moreover when a seller possesses superior information about the likelihood of entry it is shown that the length of the contract may act as a signal of the true probability of entry

rents dissipation and lost treasures comment in an interesting recent paper dari mattiacci and parisi 2005 extended tullock s 1980 rent seeking game with an entry decision the mixed strategies identified by dari mattiacci and parisi for the case of increasing returns in the contest success function r2 do not constitute an equilibrium of the game they study however these strategies are an equilibrium if the strategy space of the game is restricted by a minimum expenditure requirement and this minimum expenditure requirement is an element of a specific interval

treble damage awards in private lawsuits for price fixing the traditional model for assessing the effects of treble damage pena lties on price fixing is reexamined and shown to yield surprising res ults unless the probability of detection is extremely sensitive to the price charged increasing the damage multiple will affect neither market efficiency nor expected distribution and will raise the mark et price copyright 1987 by university of chicago press

a study of cartel stability the joint executive committee 1880 1886 this article employs weekly time series data on the joint executive committee railroad cartel from 1880 to 1886 to test empirically the proposition that observed prices reflected switches from collusive to noncooperative behavior an equilibrium model of dynamic oligopoly with asymmetric firms together with explicit functional form assumptions about costs and demand determines the estimating equations and stochastic structure of the econometric model the hypothesis that no switch took place so that price and quantity movements were solely attributable to exogenous shifts in the demand and cost functions is then tested against this alternative and rejected

markets continuity and change in the international diamond market the international diamond cartel which presides over the production side of the industry may be the most successful and longest lasting cartel in the world the dominant company in the industry debeers has been around since 1880 and has been controlled by a single south african family the oppenheimers since 1925 eight countries produce the bulk of the world s gem diamonds and most of the producing entities within these countries conform to a set of rules this conformity is the product of over a century of careful planning and negotiation in which debeers has undertaken largely successful efforts to control the diamond trade and maximize its long term prospects the past decade has seen the end of apartheid in south africa the fall of communism in russia the opening of major mines in canada and the emergence of a worldwide movement against so called blood or conflict diamonds while these developments have pummeled the diamond industry and forced its central players most notably debeers to change the nature of their trade these changes have not affected the core dynamic of the global diamond market it remains an industry dominated by a single firm and an industry in which perhaps uniquely all of the major players understand the extent to which their long term livelihood depends on the fate and actions of the others

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

free entry and efficient rent seeking this paper concerns rent seeking and the extent to which rents are dissipated under various circumstances gordon tullock s 1967 insight that expenditures made to capture an artificially created transfer represent a social waste suggested that the cost to the economy of monopoly and regulation is greater than the simple harberger 1954 deadweight loss indeed under tullock s original formulation and in the extensions of his work by krueger 1974 and posner 1975 rents are exactly dissipated at the social level 1 is spent to capture 1 so that the total welfare loss from such activities is equal to the harberger triangle plus the rectangle of monopoly profits

impossibility of collusion under imperfect monitoring with flexible production we show that it is impossible to achieve collusion in a duopoly when 1 goods are homogenous and firms compete in quantities 2 new imperfect information arrives continuously without sudden events and 3 firms are able to respond to this new information quickly the result holds even if we allow for asymmetric equilibria or monetary transfers the intuition is that the flexibility to respond to new information quickly unravels any collusive scheme and that signals about the aggregate behavior only cannot be used effectively to provide individual incentives via transfers our result applies both to a simple stationary model and a more complicated one with prices following a mean reverting markov process

testing static oligopoly models conduct and cost in the sugar industry 1890 1914 we explore the widespread methodology of using demand information to infer market conduct and unobserved cost components under the hypothesis of static oligopoly behavior direct measures of marginal cost and conduct indicating small market power serve as benchmarks the more competitive models yield better cost estimates the best cost estimates occur when conduct is estimated as a free parameter which in turn only slightly underestimates our direct measure it also tracks the decline in market power accompanying the industry s structural changes the methodology is largely validated although partial cost information can improve its predictive power conclusions are robust to demand function

temporary natural resource cartels abstract we analyze the behavior of a nonrenewable resource cartel that anticipates being forced at some date in the future to break up into an oligopolistic market in which its members will then have to compete as rivals under reasonable assumptions about the value function of the individual firms in the oligopolistic equilibrium that follows the breakup we show that the cartel will then produce more over the same interval of time than it would if there were no threat of dissolution and that its rate of extraction is a decreasing function of the cartel s life that there are circumstances under which the cartel will attach a negative marginal value to the resource stocks in which case the rate of depletion will be increasing over time during the cartel phase that for a given date of dissolution the equilibrium stocks allocated to the post cartel phase will increase as a function of the total initial stocks whereas those allocated to the cartel phase will increase at first but begin decreasing beyond some level of the total initial stocks

what determines cartel success following george stigler 1964 many economists assume that incentive problems undermine attempts by firms to collude to raise prices and restrict output but the potential profits from collusion can create a powerful incentive as well theory cannot tell us a priori which effect will dominate whether or when cartels succeed is thus an empirical question we examine a wide variety of empirical studies of cartels to answer the following questions 1 can cartels succeed 2 if so for how long 3 what impact do cartels have 4 what causes cartels to break up we conclude that many cartels do survive and that the distribution of duration is bimodal while the average duration of cartels across a range of studies is about five years many cartels break up very quickly i e in less than a year but there are many others that last between five and ten years and some that last decades limited evidence suggests that cartels are able to increase prices and profits to varying degrees cartels can also affect other non price variables including advertising innovation investment barriers to entry and concentration cartels break up occasionally because of cheating or lack of effective monitoring but the biggest challenges cartels face are entry and adjustment of the collusive agreement in response to changing economic conditions cartels that develop organizational structures that allow them the flexibility to respond to these changing conditions are more likely to survive price wars that erupt are often the result of bargaining issues that arise in such circumstances sophisticated cartel organizations are also able to develop multipronged strategies to monitor one another to deter cheating and a variety of interventions to increase barriers to entry

efficient rents 1 rent seeking behavior in the long run we have analyzed long run behavior in rent seeking under several conditions and behavioral hypotheses the question of interest is whether or not the long run expenditures will exactly equal the value of the rents our results depend on the type of competitive response which is assumed to exist in the long run and on the r value governing the probability of winning

naked exclusion comment the ability of an incumbent firm to deter entry by writing exclusionary contracts with customers has been a subject of contention in the antitrust literature the courts concern with such exclusionary contracts has been challenged by those who argue that an incumbent faced with buyers whose interest is to promote entry and competition would have to pay buyers more for the inclusion of exclusionary provisions than it could possibly gain from exclusion in a provocative article eric b rasmusen et al 1991 henceforth rrw have argued that an incumbent may in fact be able to exclude rivals profitably using such contractual provisions because it can exploit buyers lack of coordination in essence if buyers expect other buyers to sign such provisions then they may see little reason not to do so themselves the rrw argument is potentially an important one because most alleged instances of entry deterrence through exclusionary contracts with customers occur in situations with multiple buyers unfortunately however rrw s two main results contain errors in this note we reconsider the rrw model providing correct characterizations of the likelihood and cost of exclusion for an incumbent firm our results indicate that while the intuition suggested by rrw is valid the equilibrium likelihood and cost of exclusion differ from what rrw derive moreover our analysis illuminates some further aspects of exclusionary contracting with multiple buyers among these issues we focus on how an incumbent can use discriminatory offers to exploit the externalities that exist among buyers in the provision of competition in section i we review the basic assumptions of the rrw model in sections ii and iii we then consider in turn the cases of simultaneous and sequential offers studied by rrw for the simultaneous model we distinguish between settings in which the incumbent can and cannot discriminate in its offers to different buyers this distinction is the source of the problem in rrw s analysis their simultaneous offer model assumes no discrimination but the proof of their proposition 2 assumes at times that discrimination is feasible we show that absent the ability to discriminate the incumbent can exclude profitably only when buyers fail to coordinate on their most preferred continuation equilibrium in contrast we show that when discrimination is possible the incumbent need not rely on a lack of buyer coordination to segal department of economics landau building stanford university stanford ca 94305 e mail ilya segal stanford edu whinston department of economics northwestern university 2003 sheridan road evanston il 60208 e mail mwhinston nwu edu we thank eric rasmusen john wiley and participants in the berkeley stanford iofest the university of copenhagen vertical restraints conference and a seminar at the antitrust division of the u s department of justice for helpful comments we thank federico echenique for excellent research assistance 1 for example a recent department of justice investigation concerned the use of exclusive contracts by the leading provider of computerized ticketing services ticketmaster most major cities have several large concert sports venues in many cities ticketmaster has exclusive contracts with a very large share of these venues 2 the other leading response to the argument that contracts with buyers cannot be a profitable method of exclusion is given in philippe aghion and patrick bolton 1987 section i one factor limiting the applicability of the aghion and bolton theory however is that it involves partial exclusion the contracts signed are not fully exclusionary they involve finite stipulated damages and the profitability of the strategy arises from extracting rents from an entrant when entry occurs indeed in the aghion and bolton model contracts that fully exclude offer no benefits over writing no contract at all in section iii of their paper aghion and bolton also discuss a two buyer version of their model in which externalities arise across buyers in contrast to the analysis here and in rrw they allow the incumbent to make an offer to a buyer i that is conditional on the acceptance decision of the other buyer 3 r innes and r j sexton 1994 also discuss the use of discriminatory offers in the context of a model in which buyers can form coalitions with the entrant

long run equilibrium and total expenditures in rent seeking the lure of excess profits or rents associated with monopoly power gives rise to expenditures to obtain these rents competitive rent seeking behavior is recognized as a factor which must be included among the wastes associated with monopoly power tullock 1967 posner 1975 1 the expenditures are aimed at transferring wealth rather than its creation and the use of resources to obtain this transfer is a loss to society how important rent seeking is as a part of the total monopolistic waste hinges on the size of the total expenditures induced by a given level of excess profits

a two part sample selection model of british bilateral foreign aid allocation the allocation of british bilateral foreign aid among developing countries is simultaneously modelled focusing on allocations during the period 1980 87 two aid allocation decisions are analysed using a variant of the lee maddala econometric model the first decision concerns the determination of developing country eligibility for aid while the second concerns the amount of aid eligible countries are allocated given the implied two part decision making process sample selection techniques are employed it is hypothesized that british bilateral aid eligibility and amount decisions are based on bristain s humanitarian commercial and political interests in developing countries results obtained indicate that these decisions are generally consistent with each of these interests especially those relating to the political importance of commonwealth members

tullock s rent seeking contest with a minimum expenditure requirement we consider a rent seeking contest of the kind introduced by tullock 1980 in which two players compete for a monopoly rent we extend the contest by requiring that if a player puts forward an effort his expenditures must be larger than or equal to some minimum level we show that depending on the model parameters the number of nash equilibria of the extended model can be zero one two or four furthermore it turns out that the extent of rent dissipation in a nash equilibrium of the extended model can be larger than equal to or smaller than the extent of rent dissipation in the unique nash equilibrium of the original model

the impact of cyclical demand movements on collusive behavior recent work by rotemberg and saloner 1986 investigates the effect of the business cycle on optimal collusive pricing by specifying that demand is subject to i i d shocks an implication of the i i d assumption is that firms expectations on future demand are unrelated to the current level of demand we put forth a model that allows for both the level of current demand and firms expectations on future demand to change over time thus it captures two important properties of the business cycle our analysis reveals that while the gain to deviating from a collusive agreement is greatest during booms firms find it most difficult to collude during recessions as the forgone profits from inducing a price war are relatively low an implication of this effect for pricing behavior is that at the same level of demand price is lower when demand is declining than when demand is rising consistent with previous theoretical work we find that firms price countercyclically for a range of values for the discount factor however numerical simulations reveal a greater tendency for firms to price countercyclically during recessions than during booms

efficient rents 2 free entry and efficient rent seeking in the competition for a monopoly right in which the number of bidders is fixed tullock and others have found the value of the resources spent in the aggregate to capture the transfer to be sometimes less than and sometimes greater than the value of the monopoly we think this approach to be incomplete since it leaves unanswered the question of what determines the number of individuals who will vie for the right to be the monopolist it is unsatisfactory to imagine for example that the franchisor sets the number of contestants one could then foresee that rent seeking would arise to influence the permissible number of bidders and this merely moves the rent seeking dissipation question one step back