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Are athletes doped? Some theoretical arguments and empirical evidence.
Article Type:
Report
Subject:
Drugs and athletes (Control)
Drugs and athletes (History)
Sports medicine (History)
Sports medicine (Laws, regulations and rules)
Mandatory drug testing (Methods)
Athletic ability (Management)
Authors:
Dilger, Alexander
Frick, Bernd
Tolsdorf, Frank
Pub Date:
10/01/2007
Publication:
Name: Contemporary Economic Policy Publisher: Western Economic Association International Audience: Academic; Trade Format: Magazine/Journal Subject: Business; Economics Copyright: COPYRIGHT 2007 Western Economic Association International ISSN: 1074-3529
Issue:
Date: Oct, 2007 Source Volume: 25 Source Issue: 4
Topic:
Event Code: 930 Government regulation; 940 Government regulation (cont); 980 Legal issues & crime; 200 Management dynamics Advertising Code: 94 Legal/Government Regulation Computer Subject: Government regulation; Company business management
Geographic:
Geographic Scope: United States Geographic Code: 1USA United States

Accession Number:
180372671
Full Text:
Sports fans all over the world have recently witnessed an increasing number of spectacular doping cases, leading to considerable annoyance in the public. However, our knowledge regarding the prevalence of doping is still quite limited, leading some people to speculate that (nearly) all professional athletes are doped and possibly even have to be doped to be good enough to compete successfully in highly selective tournaments. On the other hand, particularly representatives of the sports associations pretend that since the number of positively tested athletes remains small, there are only a few "black sheep," while in general, the world of sport is clean and fair. In the recent past, a number of theoretical models have been developed that can be empirically tested, which, in the end, may lead to the formulation of policy recommendations (ranging from higher sanctions to legalizing doping). We review the more important models and present anecdotal as well as some quantitative empirical evidence on the prevalence as well as the determinants of doping. (JEL K42, L83, M52)

1.INTRODUCTION

It is commonly acknowledged that rankorder tournaments not only have desirable features--such as inducing high effort levels among participants--but also share characteristics that can be quite problematic: the more skewed the structure of the rewards is, the more incentives the contestants have to engage in activities that are not in the interest of the organizer (Lazear and Rosen, 1981; Nalebuff and Stiglitz, 1983; O'Keefe, Viscusi, and Zeckhauser, 1984). Examples of such activities include plagiarism and manipulation of research results by academics, fraudulent accounting by managers, mobbing and sabotage by "normal" employees competing for a promotion, and the use of steroids and other performance-enhancing drugs by professional athletes. What all these situations have in common is that a number of individuals compete for a given winner prize (be it a tenure-track position, a significant pay increase, an appointment to an attractive position, or a gold medal). Moreover, in each of these situations, the contestants usually have the opportunity of increasing their individual success probabilities by developing activities that are illegal and, therefore, unacceptable. The economic consequences of these kinds of behavior can be quite significant as it will very often lead not only to a misallocation of talent but also to a decrease in incentives, given that contestants can observe the "cheating"1.

Since individual athletes can improve their probability of winning not only by the right kind of training but also by using banned or illicit substances that enhance performance, it is difficult to distinguish between performance that is to be attributed to talent and hard work and performance that is due to illegal preparation, that is, doping (cf. Preston and Szymanski, 2003, pp. 612-613). Assuming that event organizers as well as spectators have a preference for "clean" athletes,(2) separating the two sources of performance is crucial for obvious reasons: as can be currently seen in one of the most doping-prone disciplines--professional cycling--sponsors as well as fans seem to be disgusted by the behavior of many (possibly even most) riders.(3) While the former reduce their financial support or withdraw completely from the sport (like the owner of the Swiss top team "Phonak"), the latter increasingly refuse to watch the races either live or on television (during the recent 2006 Tour de France--the most prestigious multistage race--TV ratings plummeted to a record low in most European countries).

After a brief review of the history of doping methods and scandals (Section II), the article proceeds as follows: in Section III, we compare different microeconomic approaches to modeling the behavior of rational athletes; Section IV presents some empirical evidence consistent with the theoretical reasoning; and Section V concludes.

II. THE HISTORY OF DOPING METHODS AND SCANDALS

A. Past and Recent Doping Methods

The term "doping" is commonly used to describe the nontherapeutic use of legal substances (like caffeine(4)), illegal ones (like cocaine), and drugs (like erythropoietin [EPO]) to improve athletic performance. Doping is, therefore, a particular form of "cheating," that is, the intentional and deliberate violation of implicit or explicit rules to create an "unfair" advantage in one's own interest and at the expense of others.

Doping is certainly not a recent phenomenon: Greek wrestlers and Roman gladiators tried to improve their physical strength by eating sheep's testicles. As early as the late 19th century, professional cyclists were using substances like caffeine and cocaine to improve their performance, reduce pain, and delay fatigue. In the early 20th century, heroine and cocaine were used widely by professional athletes until they became available only on prescription. In the 1930s, amphetamines replaced strychnine, a drug that, in combination with brandy, had nearly killed Olympic marathon runner Thomas Hicks in 1904. In the 1950s, Soviet athletes started to use male hormones, with the Americans following soon with steroids. More recently, anabolic steroids (e.g., used by many baseball players as well as by track and field athletes) have been replaced by "blood doping," especially with EPO, as the most prominent way of "artificially" improving athletes' performance (cf. Wagner, 2000).

Testing for illegal substances has become a "big business," with athletes trying to hide or mask their use from officials, fans, and fellow competitors, while laboratories are developing additional and more sensitive procedures, allowing to detect even small residues of illegal drugs and substances. Thus, detecting drug use and evading detection have become a contest in itself, leading to a specific form of an "arms race": since in the meantime it can even be determined if the body's hemoglobin level has been influenced by blood doping, athletes have recently switched from using normal therapeutic doses to "rnicrodosing," which means that substance use can be detected only within a very short period of time. Moreover, athletes can apparently mask substance use by introducing protease enzymes, for example, that destroy traces of EPO in human urine (cf. Schmidt et al., 2000).

B. A Selective Survey of Recent Drug Scandals

Since doping has always been and continues to be particularly prevalent in cycling and track and field, we restrict ourselves here to the most prominent offenders from these two sports that attract particularly large numbers of spectators and large amounts of money from sponsors and TV stations. (5) Before presenting some systematic evidence on the doping behavior of athletes (see Section IV), we list a number of spectacular cases that occurred in the recent past in these two sports.

Cycling.

* During the 1967 Tour de France, British rider Tom Simpson collapsed during the ascent of the Mont Ventoux. Despite immediate medical treatment, Simpson died. Two tubes of amphetamines were found in the rear pocket of his racing jersey.

* In 1998, the entire Festina team was excluded from the Tour de France following the discovery of a team car with large amounts of various performance-enhancing drugs. The team director later admitted that some of the cyclists were routinely given banned substances.

* More recently, David Millar, the 2003 World-Time Trial Champion, admitted using EPO. He lost his title and was suspended for 2 yr. Still later, Roberto Heras was stripped of his victory in the 2005 Vuelta a Espana and suspended for 2 yr after testing positive for EPO.

* In 2006, Spanish police arrested five people, including the sporting director of the Liberty Seguros cycling team, on charges of running a massive doping scheme involving most of the team and many other top cyclists. Several potential contenders in the 2006 Tour de France, such as Jan Ulrich, Ivan Basso, and Oscar Sevilla, were forced to withdraw.

* Less than a week after the 2006 Tour de France, it was revealed that winner Floyd Landis had tested positive for an elevated testosterone-to-epitestosterone ratio after his stunning victory on Stage 17. A second test confirmed the preliminary findings of deficient levels of epitestosterone. A decision to strip Landis of the title is still pending.

* In September 2006, some former teammates of Lance Armstrong admitted that they had taken EPO during the 1999 Tour de France. While they did not state that Armstrong had done the same, the press attacked Armstrong, who throughout his career had been a target of doping allegations.

Among the 20 teams that are currently admitted to the "Pro Tour," the highest league in professional cycling, 9 are managed by former riders who have been found guilty of doping (AG2R Prevoyance, Astana, Discovery Channel, Gerolsteiner, Quick Step, Rabobank, T-Mobile, CSC, and Credit Agricole). In the years 1940-2005, about 600 different riders have been found cheating, among them some 75 individuals who have been tested positively more than once (http://www.cycling4fans. com).

Track and Field.

* During the 1970s and 1980s, many athletes from Eastern bloc nations were suspected of augmenting their ability with some kind of pharmacological help (some of the world records in the track and field disciplines are now more than 20 yr old). After the fall of communism in Eastern Europe and the reunification of Germany, documents surfaced, proving that the East German sport establishment had conducted systematic doping of virtually all its world-class athletes.

* Canadian sprinter Ben Johnson failed the drug test when anabolic steroids were found in his urine after his victory in the 100 m at the 1988 Summer Olympics. He later admitted to have taken other drugs and human growth hormones as well. Carl Lewis was promoted one place to take the Olympic gold medal. Later, it was revealed that he also had been using drugs.

* 100 m world champion Katrin Krabbe was found guilty of having used anabolic steroids in 1992 at least two times.

* In 1999, Olympic champions Dieter Baumann (5,000 m) and Linford Christie (100 m) failed drug tests and were found guilty of using Nandrolone, an anabolic steroid.

* At the Olympic Games 2004 in Athens, Greek sprinters Kostas Kenteris and Ekaterini Thanou feigned a motorcycle accident to avoid a doping test. The Hungarian hammer thrower Adrian Annus was deprived of the gold medal because he manipulated his first doping test and refused a second one. The Hungarian discus thrower Robert Fazekas lost his gold medal after avoiding a first doping test and trying to swap the urine sample in the second one.

* In July 2005, the founders of "Bay Area Laboratory Co-operative," based in California, admitted the production and distribution of anabolic steroids. Those implicated or accused in the ensuing scandal included track and field athletes Dwain Chambers, C. J. Hunter, Marion Jones, and Tim Montgomery.(6)

* On July 29, 2006, 100 m Olympic and world champion Justin Gatlin failed a drug test.

Much of the (economics) literature on the use of drugs in sport is, at best, based on anecdotal evidence. The lack of rigorous evidence, however, is not surprising as athletes taking substances know that they are doing something that is taboo, illegal, and sometimes highly dangerous. Nevertheless, the rewards to winning combined with the increasing effectiveness of the available drugs and the consistently low rate of detection create a "cheating game" that could be irresistible to most (professional) athletes as the next section of our article shows.

III. A REVIEW OF THE THEORETICAL LITERATURE

There are currently four different, though closely related, topics in the economic analysis of doping. First, some authors still try to find a convincing definition of the term (see above) by distinguishing it from other (legal) activities such as training at high altitude and specific diets. Second, there is much interest in the incentives that lead athletes to use illegal substances. This leads to the third (and most pertinent) question: how can these incentives be altered; which factors advance, and which ones prevent doping? Fourth, it is worth analyzing why doping is strictly forbidden and whether it is possible or desirable to stop athletes using illicit medication. Most economists are interested in the second and third questions only as they have some expertise analyzing incentives and the ways these have to be designed to elicit the desired behaviors.(7) However, all the four issues are closely related: it is certainly difficult to explain why athletes are doping and how such behaviors can be prevented without some convincing definition of the term doping. Conversely, if doping only means consumption of illicit medication, then the abolition of these rules would solve all doping problems by definition.

Breivik (1987) is the first to characterize the doping problem as a potential prisoners' dilemma.(8) Doping by one athlete raises his probability of winning, whereas doping by other athletes decreases that probability. If all athletes use illicit medication, their individual probabilities of winning are more or less the same compared with a situation where everybody refuses to take performance-enhancing drugs. But in case they all dope, all have to bear the costs of doping. These costs include all discounted future health problems generated by doping.(9) However, most athletes do not care much about these costs because of a high preference for the present and also a very strong preference for winning (Bird and Wagner, 1997). Haugen (2004, p. 68) cited Andrews (1998) who reported findings initially presented by sports journalist Bob Goldman: more than half of 198 U.S. top athletes admitted that they would take drugs if that made them a winner for 5 yr without being detected even if they certainly died after these 5 yr due to the side effects of doping (without these side effects, only two declined to take such hypothetical drugs). Other costs of doping are the procurement costs, the moral costs of norm infringement, and, last but not the least, the expected costs of detection and punishment. In a world without a ban on doping and, therefore, without this last kind of cost (and perhaps also without moral costs), doping would possibly be a dominant strategy for all athletes (Daumann, 2003). This, in turn, implies the existence of a prisoners' dilemma because all athletes have to bear the remaining costs of doping without changing their individual win probabilities. Even if the tournament setting is a repeated prisoners' dilemma, this is unlikely to result in a doping-free world because the individuals' incentives not to cheat are weak and the existence of end-game effects guarantees that at least some athletes will continue doping.

It follows that an external institution is required to prevent doping by closely monitoring athletes and by punishing those who are detected. Even without direct punishment of doping offenders, such an institution could improve the conditions for collusion among the athletes, for example, by requiring athletes to keep a "drug diary" in which they have to include all the (legal and illegal) substances they are using (this instrument was first proposed by Keck and Wagner [1990] and Wagner [1994]). Nevertheless, even with a drug diary, some punishment is required if an athlete is found guilty of having consumed a drug not included in his/her diary. Bird and Wagner (1997, p. 759), therefore, suggested the introduction of a "peer monitoring system," where any two athletes may accuse a third one of not having listed all the drugs he/she had been using recently. The accused athlete will then be tested accordingly. In order to avoid false accusations, the two whistleblowers will be punished if the accused athlete is found not guilty. A further possible solution of the doping problem would of course be a reduction of the incentives to win by lowering the prize money that is at stake in a particular competition. The obvious disadvantage of such a strategy is that it not only reduces the incentive to dope but also and primarily the incentives to train and to pursue an athletic career. Therefore, the costs of doping should be increased by punishing any athlete who is found guilty of having used medication that is included in a "negative list" of illicit substances and procedures.(10) This list, in turn, should be updated constantly by offering bonus payments to anyone who develops and/or brings to the sporting associations' attention new drugs that significantly and measurably enhance the individual's performance. Such innovation bonuses are likely to reduce the monopoly rents of innovators of new drugs and--indirectly--the incentive to search for such innovations in the first place (Daumann, 2003).

Haugen (2004) also interpreted doping as a binary choice variable in a prisoners' dilemma framework. In the simple case of two equally talented and trained athletes and a winner's prize a, both athletes receive an expected value of 1/2a if they refrain from doping. If one athlete dopes, he is detected with probability r and has in this case to incur costs c, implying expected costs of doping re. However, if only one athlete dopes while the other does not, the former wins with certainty and gets a - re in total, whereas the clean athlete gets nothing.(11) Finally, if both athletes are doped, their individual success probabilities are 1/2 again, but both have to bear the expected cost of rc, (12) resulting in expected benefits of 1/2a-rc for each of them. This is lower than 1/2a, implying that doping is inefficient. Nevertheless, doping is the dominant strategy for both athletes as long as 1/2 a [greater than] re. Given the high prize money a and the low detection probability r, this is probably true in most professional sports today (but the symmetry of the athletes involved may be lacking).

The game-theoretical model of Berentsen (2002, p. 110) is more sophisticated.(13) He also analyzed the case of two athletes who "simultaneously and secretly decide to use a performance-enhancing drug before competing." However, this does not necessarily imply the existence of a prisoners' dilemma because doping is not a dominant strategy for heterogeneous players, which, in turn, improves the possibilities to prevent doping. Berentsen (2002, p. lll) made a strong case for doping prevention by arguing that it never increases overall welfare. Moreover, "the'wrong'player [the one with less talent] may win the game because doping changes the probabilities of winning." A particular problem that deserves special attention is "that doping tests sometimes provide faulty information. Occasionally, tests indicate that the athlete is not doped when he or she is or that an athlete is doped when he or she is not" (Berentsen, 2002, p. 111). This, in turn, is a strong argument against the simple advice that by raising sanctions, the extent of doping could be reduced.

Although the model developed by Berentsen (2002) is quite complex, its intuition is straightforward. He first defined "a critical value [tilde.C]" as the ratio of the costs of doping c and the (higher) value of winning a. This is compared to [[delta].sub.1]], defined as "the effectiveness of performance-enhancing drugs in the sense of measuring the increase of player s winning probability when only player i dopes" (Berentsen, 2002, p. 112). Without doping, Player 1 may be at least as good as Player 2, implying that his individual win probability is at least .5. If he dopes and Player 2 does not, this probability raises by [[delta].sub.1]. Conversely, the win probability of Player 2 rises by [[delta].sub.2] if he alone dopes. Moreover, Berentsen (2002, p. 112) assumed "that performance-enhancing drugs are more effective for the weak player, i.e., that [[delta].sub.2] [greater than or equal to] [[delta].sub.1]," which holds even if the physical performance of both athletes is improved to the same extent.

If [[delta].sub.1]]>[tilde.c], doping is cost-effective (too cheap relative to its effectiveness) and both athletes will dope with certainty. If, however, [[delta].sub.2]] < [tilde.c], doping does not pay and both athletes will remain clean. If [[delta].sub.1] = [tilde.c], either both athletes may dope or only Athlete 1 may do so. If [[delta].sub.2] = [tilde.c], both athletes may abstain from doping or only Athlete I does, whereas Athlete 2 dopes. If [[delta].sub.1] = [[delta].sub.2] = [tilde.c], all four variants so far are possible equilibria. Most interesting, however, is the remaining case where [[delta].sub.1].>[tilde.c]>[[delta].sub.1]] because it represents a mixed strategy equilibrium. Here, Athlete I dopes with probability [alpha] = ([[delta].sub.2]-[tilde.c])/([[delta].sub.2]-[[delta].sub.1] and Athlete 2 with probability [beta] = ([tilde.c]-[[delta].sub.1]/([[delta].sub.2]-[[delta].sub.1]). Athlete 1 dopes with a higher probability than Athlete 2 ([alpha] > [beta]) if the performance-enhancing drugs are sufficiently effective, that is, if [[delta].sub.1]+[[delta].sub.2] > 2[tilde.c]. Who of the two athletes wins with a higher probability also depends on the parameter values: if [square root of ([[delta].sub.1][[delta].sub.2])] < [tilde.c], the more talented player (Athlete 1) is less likely to win with doping opportunities than without. If both conditions are combined, the favorite is more likely to use performance-enhancing drugs than the underdog; yet, he is less likely to win with doping opportunities than without (Berentsen, 2002, p. 113), a result that is counterintuitive. (14)

Moreover, Berentsen (2002) found a nonmonotonic response to sanctions for defaulted dopers. Whereas other authors recommended increasing sanctions as a panacea against doping without further qualification, Berentsen showed that this holds only for very high sanctions: there is always a level of sanctions S that deters from doping, but this level can be extremely high,, especially if the incentive to win a is large. One may indeed be tempted to support the idea of very high sanctions for doped athletes, but as long as there are wrongly positive test results for clean athletes with probability [[theta][sub.nd], sanctions can be too high and can violate the participation constraint such that talented athletes refuse not only to dope but also to enter the competition.

Below this doping-preventing threshold, higher sanctions can even raise instead of reduce the probability of doping, especially for the less talented Athlete 2. With some restrictions on the parameter space of the general model, the following holds: without any sanctions or s:=,S/a below a threshold [[sigma].sub.1], both athletes dope with certainty. With s ranging between [[signma].sub.1] and [[sigma].sub.2] the better Athlete 1 dopes with certainty and the less gifted Athlete 2 refuses to dope. For [[sigma].sub.1]] < s < [[eta[sub.3], there are mixed equilibria in which both athletes are doping with some probability that is decreasing in s for Athlete 1 and increasing in s for Athlete 2. If [[sigma].sub.3]] < s < [[eta[sub.4], Athlete 2 dopes with certainty, while Athlete 1 refuses to dope. Finally, only s > [[alpha].sub.4] guarantees a sport that is free of doping, [alpha] is rising in the effectiveness of doping 6 and decreasing in the quality of the test technology, that is, the probability [[theta].sub.d] by which a doped athlete can actually be identified. Interestingly, a higher p, the win probability of Athlete 1 in case nobody is doping, leads to additional mixed equilibria because it lowers [[alpha].sub.1] and [[alpha].sub.2] while raising [[alpha].sub.3] and [[alpha].sub.4].

Moreover, Berentsen (2002) showed that an identical level of sanctions S for a positively tested winner and the loser of a contest is not adequate. For some specific parameter constellations, identical sanctions can either not prevent doping or violate the participation constraint of the weaker Athlete 2. In the model, the ranking-based punishment scheme [s.sub.1] = (1-[[theta].sub.d] - [[theta].sub.nd] + [[theta].sub.nd.sup.2] - [[tilde].c])/[[theta].sub.d] and [s.sub.2] = 0 is a perfect mechanism (Berentsen, 2002, p. 113), where [S.sub.1] = [s.sub.1] a is the sanction for the winner if he or she is positively tested and [S sub 2] = [s sub 2] a is the sanction for the loser if positively tested. The recommendation therefore is to treat winners and losers differently and to probably abandon punishments and doping tests for the losers. Even if the tests have to be performed before the winner has been identified, it is possible to prevent doping with fewer tests and thereby lower costs by simply differentiating the sanctions. This is in line with the policy of most sports associations that all winners but only some losers have to attend a test after the competition. Even if the verdicts for positively tested winners and losers are identical (mostly a temporal ban), this hurts the winners much more than the losers because the former may have to return their prize money and are very likely to lose most of their lucrative endorsement contracts.

A major shortcoming of the analysis is that the author did not model the impact of a "windfall-profit effect" (Krakel, 2007) that arises when the winner prize is awarded to the loser in case the winner got defaulted due to doping while the loser proved to be clean. Such a policy is a strong incentive to abstain from doping and to hope that the competitor dopes instead.(15)

Berentsen and Lengwiler (2004) analyzed evolutionary doping games with different types of players. Players can be either strong or weak, with a given probability q, and are matched randomly with either another strong or another weak player in a contest. If both are strong or both are weak, then their win probabilities without any doping are 1/2. If a strong player is matched to a weak one and both are either doped or clean, the former wins with certainty. If one player, weak or strong, is doped and the other one is not, the doped one wins with certainty. Finally, if both players are doped, their win probabilities are unchanged compared to the situation in which both are clean. Contrary to most other models, the players in this evolutionary game do not choose their best possible strategy but are "programmed" to follow a pure strategy, that is, they are either doping all the time or always stay clean. As long as one of the two strategies has a higher expected value than the other one, it proliferates at the expense of that other strategy. In equilibrium, both strategies have to be equally good or one will disappear, at least for one type of players. The interesting result of this model is that anything can happen depending on the parameter values.(16) There are equilibria where all players are doping; in others, nobody dopes; and in still others, only the strong or only the weak athletes take drugs. Finally, there can be cycles in which doping is used for a while and not at other times. The intuition here is that a strong player matched with a weak one only wants to dope as long as the weak one does, who, in turn, is only interested in doping as long as the strong one stays clean.

Dilger and Tolsdorf (2004, 2005) chose a much simpler and at the same time very general approach derived from decision theory instead of game theory.(17) This allowed them to model quite easily the behavior of a large number of athletes instead of just two. Here, each athlete makes his decision by taking the behavior of the other contestants as given. This is not quite correct because the opponents' decisions are not independent of the individual's decisions (which is, of course, fully recognized in game-theoretical models). Nevertheless, one can search for an equilibrium in which the beliefs of all participants are mutually consistent. As long as game-theoretical models with many players are too complex to be solved even by the most gifted economists,(18) professional athletes' behavior may be consistent with these models as they will have to use simpler heuristics and therefore find the decision-theoretical one particularly appealing. It simply lumps together the different factors that influence the utility of an athlete. That utility will then be maximized taking into account the potential costs and benefits of doping.

The utility without doping can be written, for example, as [[mu].sub.nd] = pa + r, where p is the probability of winning, a the utility from winning, and r is the utility that is derived from being an athlete who can be either positive (e.g., due to the joy of just doing it) or negative (e.g., due to the opportunity costs of time). The utility with doping is [u.sub.d] = (1-[[theta].sub.d])(p + [delta])a + r-[[theta].sub.d]S-c, where [[theta].sub.d] is the probability that a doped athlete is detected, [delta] is the higher win probability induced by doping, S the utility loss, and c is all other costs of doping like drug prices, health risks. If one is interested in any other effect, for example, the probability [[theta].sub.nd] that a clean athlete is tested positive, it is easy to add that to the model. Comparing the utility levels with and without doping, an athlete will dope if and only if [[delta].sub.a]-[[theta].sub.d](p+[delta])a - [[theta].sub.d]S-c > 0. It is simple to derive from this a number of direct effects:(19) more effective drugs, a higher level of prize money, a lower detection probability, a lower initial probability of winning, lower sanctions, and lower doping costs will all increase the probability of doping. This is also to be expected when competition increases and in case of athletes who are close to the end of their careers.

In a number of recent articles, alternative mechanisms to deter doping have been discussed.

* Tietzel and Muller (2000) argued that "negative lists" including all the substances that are (currently) forbidden exaggerate the doping problem as they reward the search for and development of new substances to substitute the forbidden ones. Therefore, they propose a "fairness-treaty" between sport associations and sponsors as a potential solution: sport associations and promoters should ban positively tested athletes forever,(20) while sponsors should pay for the application and the further development of (better) doping tests. These suggestions are not very convincing for a number of reasons: if the recommended treaty was helpful in the fight against doping, it would have been concluded in the meantime. Moreover, a lifelong ban for one positive test is problematic as it neglects the possibility of a wrong test result. Finally, the doping dilemma remains the same irrespective of whether the state tries to solve it with laws or sport associations try to do so with voluntary treaties.

* Meannig (2000, 2002) suggested that professional athletes should pay part of their prize money into a fund. That money will eventually be paid back to athletes who stayed clean over their careers after they have retired. Thus, athletes should post bonds that will be forfeited if they are caught cheating (this is similar to the deferred compensation model developed by Lazear [1979]). The main advantage of this proposal is that older athletes at the end of their career can effectively be deterred from doping because they have more to lose than younger athletes. This, in turn, is likely to avoid any end-game effects. Finally, Maennig proposed the introduction of a "positive list" including drugs that are explicitly allowed. Anything that is not included in that list would, therefore, be illegal and its use be punished. Although this will slow down the pace at which new drugs will be developed, it will certainly lead to an increase in the number of cases of "unintentional" doping.

* Prinz (2005) questioned whether there is any meaningful difference between doping and training because in both cases, a "competition paradox" exists that, in turn, results in a particular dilemma--a systematic difference between individual and collective rationality: whether an athlete trains or dopes, he always produces a negative externality for his opponents. While in the case of training this is honored by organizers, sponsors, and spectators, this is most likely not the same in case of doping. However, if the "gladiator effect" (Prinz, 2005) really exists (fans are interested only in the winner and not in the way success has been made possible) and is sufficiently strong, then "the war against doping" is already lost (and it may, therefore, be legalized).

* Osborne (2005) pointed out that training is very often more detrimental to an athlete's health than doping and that in many sports, harming the health of opponents is even the ultimate goal (such as in boxing). Therefore, the case that has been made against doping so far is not a very convincing one. He suggested another explanation: fans not only want to see an excellent athletic performance but also want to see athletes expending a lot of effort. Doping very often is not only complementary to effort but also a potential substitute.(21) Thus, fans want to be able to distinguish between "honest" athletes working hard and "lazy dopers" able to deliver a possibly even better performance. If fans expect that athletes replace hard work by using drugs, their utility and, therefore, their willingness to pay will be considerably reduced. As a result, athletes as well as sporting associations have an incentive at least to pretend that the sport is free of doping.

IV. A REVIEW OF THE (RARE) EMPIRICAL EVIDENCE

Apart from one notable exception, systematic empirical evidence on the frequencies of doping or its determinants is not yet available. This is not surprising, given the "illegal" character of using performance-enhancing drugs. To the best of our knowledge, only two further studies exist so far that attempt to test some of the implications derived from the models presented above.

Pitsch, Emrich, and Klein (2005) reported the results of a www.survey in which they applied the randomized response technique to elicit information on the prevalence of doping among German elite athletes. Based on a rather large sample with about 450 respondents, they found that approximately half of the population had at some stage of their careers used doping. The percentage of dopers among athletes competing at the national level is only estimated at 42%, and among athletes competing at international level, the respective share is 58%.

Dilger and Tolsdorf (2005) used an unbalanced panel of 64 world-class sprinters who participated in 3,024 different 100-m races during the period 1997-2002. Of these 64 athletes, 16 (25%) have been tested positively at some stage during these six seasons. Controlling for a number of other (potential) determinants of individual performance (such as the importance of the particular event, weather conditions, stage of the tournament, i.e., heat vs. final),(22) they found that athletes who have been found cheating participated in a significantly lower number of races (28 vs. 54) than observationally similar but clean athletes.(23) Apparently, doped athletes fear detection and, therefore, enter fewer competitions than their (seemingly) clean colleagues. Moreover, athletes who have been tested positively are significantly older (about 3 yr), suggesting that in its present form, the threat of punishment (athletes are banned for at most 2 yr) leads to a significant increase in the probability of cheating when athletes reach the end of their careers.

The standard deviation of athletes' performance is significantly (at the 1% level) lower if they use illegal drugs (0.171 sec compared to 0.261 sec for clean sprinters). Maintaining a high level of fitness and being able to repeat an excellent performance are obviously easier under the influence of "supportive" medication. Doping seems less helpful in increasing one's potential than in using it more fully most of the time. Athletes are best in the season in which they are positively tested. This underlines that doping really improves the individual's performance. An optimistic interpretation of this result would be that most athletes are really clean most of the time and offenders are caught soon. Alternatively, the positively tested athletes may simply have exaggerated what they and most others always do (just more carefully). Finally, it may simply reflect the fact that a better performance increases the probability of being selected for a doping test.

A second study by Dilger and Tolsdorf (unpublished(24)) uses data on 187 identified cheaters from professional track and field, who got caught in the years 1999-2004, among them 7 world record holders, 9 continental record holders, 25 national record holders, 8 Olympic champions, 16 world champions, 11 continental champions and 14 national champions. The offenders came from all disciplines: 123 runners (among them 43 sprinters, 22 middle distance, 26 long distance, and 15 marathon runners as well 17 hurdle runners), 19 jumpers (among them 7 practicing pole vault, 6 long and triple jump, and 6 high jump), 39 throwers (among them 18 practicing shot-put, 7 javelin throw, 7 hammer throw, and 7 discus throw), and, finally, 6 race walkers. The study finds that the degree of competition (i.e., the "closeness" of the performance of the best 30 athletes of a particular discipline in a given year measured by the Gini-coefficient) leads to a significant increase in the number of positively tested athletes in a discipline. (25). Although the number of female athletes who have been caught cheating is considerably lower than the number of men (84 vs. 103), gender has no significant impact in the model. The reason is that in the women's contests, the degree of competition is significantly lower. This together with the significant competition variable implies that "cutthroat competition" is likely to induce behavior that most people would consider unacceptable (in accordance with the theory given in Section III).

More indirect evidence on the frequency of doping can be derived from studies by Bernard and Busse (2004) and Sterken and Kuper (2003) who tried to explain the variance in the number of medals won in the Summer Olympic Games 1960-1996 by the participating nations. Controlling for country size (log of population). country wealth (log of gross national product per capita), home advantage (host nation dummy), and lagged medal share, they found that nations that formerly belonged to the Soviet bloc were far more successful than expected. This can be attributed either to the relevance of "state doping" or to a more "lenient" control system. (26).

Summarizing, it appears that the evidence is compatible with the sometimes simple, sometimes elaborate economic models discussed at some length in this article. However, we are far from being able to present "stylized facts." As in the literature on the economics of crime, researchers have to rely on statistics that are notoriously incomplete.

V. SUMMARY AND POLICY IMPLICATIONS

In economic contests in general and in sports tournaments in particular, monitoring of the actions taken by participants is imperfect. Therefore, competition is likely to induce not just work effort (i.e., investing in the development and use of advanced training methods) but also other choices at the athlete's discretion that increase his or her success probability (i.e., cheating in the sense of taking performance-enhancing drugs). The likelihood of doping clearly depends on the payoffs in the tournament, the probability of cheating being detected, the number of contestants, and the penalty associated with being identified as a cheater.

The currently used measures to deter doping are clearly insufficient: the negative lists that are currently being used by most sports associations have the undesirable side effect to intensify the research for and the development of new drugs that enhance performance. As new substances can go undetected until a test technology has been developed, developing a positive list that includes only legal drugs does not solve the problem either: something that cannot be tested for will, by definition, not be detected. Moreover, such lists are intellectually unsatisfying as the criteria according to which drugs are either included or not accepted remain unclear.

The theoretical literature--starting from the assumption that doping occurs in a prisoners' dilemma situation--suggests that some kind of an exogenous intervention is required to deter doping. However, particularly the more elaborate models that have been deveoped recently show that everything is possible depending on the circumstances: sometimes all athletes will be doped, sometimes nobody; in some cases, the stronger athlete has an incentive to cheat, and in others, it is the weaker athlete; sometimes athletes dope with a probability of 100%, and in other situations, that probability is (much) lower.

Given the seemingly incompatible predictions that can be derived from the models, (27) it is not at all surprising that the list of recommended measures to deter doping is quite long: while the old literature clearly advocates higher sanctions to deter athletes from doping, the new models convincingly show that this is not necessarily a good idea because high sanctions can even increase the use of doping or drive clean athletes out of the sport. What would certainly reduce the amount of doping is an increase in the number of tests and further refinements of the test technologies. (28) Since the costs of testing most, if not all, athletes are--and will continue to be--prohibitive, such a scenario is unlikely (by the way, technology that helps mask the use of illegal drugs is widely available). From a theoretical point, there are at least two possible solutions to that problem. First, prizes can simply be confiscated from people found to have cheated and can be given to the best loser who has been found clean (this is done, e.g., in the Olympic Games). This has the effect of reducing the amount of monitoring required to generate an equilibrium in which neither athlete dopes (cf. Curry and Mongrain, 2005).(29) Second, organizers can ask losers "to blow the whistle," that is, the winner is only tested if he or she is accused of cheating by the loser. This will reduce the frequencies of cheating, is less costly, and leads to strict Pareto improvement if sanctions for cheating are sufficiently large (Berentsen, Brugger, and Lortscher, 2003). (30)

Unfortunately, neither of the two strategies is likely to solve the problem (completely): since the available test technologies are far from being perfect (sometimes clean athletes are tested positive and sometimes doped athletes will go undetected), variations in the parameters mentioned above--doping costs, detection probability, prize money, number of contestants, and penalties for cheaters--will at best reduce but certainly not eradicate illegal activities in sport, once considered a domain of fairness and integrity.

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ABBREVIATION

EPO: Erythropoietin

(1.) In general, doping is a problem in sports precisely because it cannot perfectly be verified. Nevertheless, contestants can often observe it more easily, while outsiders usually lack the ability to prove it to third parties.

(2.) This assumption has been heavily disputed in the past. It is, of course, also possible that organizers as well as fans want to see spectacular performances regardless of how these performances have been made possible. However, issues such as closeness of the competition, fairness, or elegance matter empirically. For fans as well as for sponsors, performance within given constraints seems important, not absolute performance as such (Konarad, 2005, p. 11).

(3.) These reactions are not unique to Europe: according to a recent opinion poll conducted by USA Today, more than 86% of American baseball fans claim that compulsory testing for steroids would renew their interest in baseball (Curry and Mongrain, 2005, pp. 20-21).

(4.) The amount of caffeine that may be consumed by an athlete prior to a competition was limited until 2005.

(5.) We deliberately disregard sports like weightlifting, for example, where recently complete national teams have been sent home from the World Championships because the majority of the athletes Tailed drug testing immediately before the opening ceremony. Moreover, we also disregard sports that are less physical and/or more technical in which doping is less useful.

(6.) Moreover, baseball players like Barry Bonds and Jason Giambi as well as several players oi' [he Oakland Raiders were also involved.

(7.) A convincing definition of the term doping seems to be more of a technical or even linguistic problem, whereas the forth issue, why doping is strictly forbidden, is considered a normative question--something that economists either like to evade or to take the answer(s) given by philosophers or politicians for granted.

(8.) Sec also Keck (1987). Moreover, Keck and Wagner (1990) argued that the prisoners' dilemma is not only confined to the individual athletes but can also be applied to explain the behavior of officials and national sports associations--with the crucial difference that the latter will not be punished if doping is detected.

(9.) Maennig (2000) explicitly mentioned only a possible loss of honor and financial losses resulting from a ban as costs of doping. Other costs are the negative externalities arising from doping, that is. the loss of credibility for other athletes. However, all these costs other than health problems would disappear as soon as doping was legalized.

(10.) Alas, the difficulty in verifying the illegal use of substances and procedures remains the same, only the definition of doping would be clearer.

(11.) Haugen (2004, p. 71) assumed "--for simplistic reasons--that the payoff received by any agent is kept even if this agent is caught in doping." This is unnecessary because c could include a, that is, the costs in case of being caught include the repayment, although this contradicts the supposition of Haugen (2004, pp. 72-74) that a is much higher than c since the financial rewards in professional sports are very high and rising, whereas periods of exclusion for caught dopers are falling and that when the typical punishment involves exclusion, there is no history of direct negative economic consequences. In any case, more problematic is the payoff of zero for the nondoped athlete because he or she would get some prize, eventually lower than a, if the doped athlete is caught. Eber and Thepot (1999) presented a model where the prize of a doped winner is given to the loser. They also modeled risk aversion and their main conclusion was that a low spread between the prize for the winner and the loser is the best remedy against doping.

(12.) It is questionable whether the expected costs are really the same for both athletes independently of winning. A winner has a higher chance of being tested than a loser and has probably more to lose by being detected. Nevertheless, this detail does not change the main result.

(13.) This is explicitly acknowledged by Haugen (2004, p. 69), who aimed at "a less technical presentation and. consequently, a potentially broader audience."

(14.) The intuition behind this counterintuitive result is that [[delta].sub.2] has to be much larger than [[delta].sub.1], otherwise both conditions cannot be fulfilled at the same time. More effective doping for the less talented player means the more talented one dopes more often to counter this effect, but there remains a disadvantage due to the mere possibility of asymmetrically effective doping.

(15.) See also Eber and Thepot (1999) and Krakel (2007).

(16.) It is an open empirical question whether these many possibilities reflect reality or whether the approach developed here offers few insights for the understanding of doping particularly because of the large number of possible outcomes.

(17.) Bourg (2000) and Maennig (2002) have first introduced such models following Becker (1968) in his famous analysis of criminal behavior.

(18.) This depends on the kind of model, of course. It holds for most models presented here, but see Bird and Wagner (1997) for an exception.

(19.) There can be indirect countereffects from the reactions of others that only a game-theoretical approach is able to identify systematically. However, the higher the number of (not too heterogeneous) contestants, the smaller the impact of any individual athlete, thereby reducing the inaccuracy of a decision-theoretical approach.

(20.) Buch (2001) also proposed the introduction of the title "doping-free athlete" as a kind of marketing tool. However, this may result in even more hypocrisy.

(21.) Konrad (2003) showed doping to be welfare enhancing under the assumption that it is a complement to other legal inputs. Krkel (2007) also analyzed the combination of doping and other inputs like training, which can result in enhanced welfare by doping.

(22.) Most of these control variables are not statistically significant. The importance of the race, the stage of the tournament, and the weight and height of the athlete all proved to be irrelevant in the estimations. However, older sprinters are significantly better than younger athletes (which might be due to a selection effect).

(23.) The assumption that those who have not been tested positively are always "clean" is, of course, problematic. Carl Lewis, who was awarded the gold medal in the 100-m dash in the 1988 Olympic Games after the suspension of Ben Johnson, later admitted that he had also been taking drugs during that time. Lewis, however, was never tested positively.

(24.) For a first sketch with a smaller data set and other desiderata, see Dilger and Tolsdorf (2004. pp. 274-278).

(25.) The study further controls for fan demand by taking into account differences in TV ratings during the last World Championships and Olympic Games and for a linear time trend. These variables as well as the age of the athletes arc not statistically significant.

(26.) Another explanation emphasizes the importance of sport funding: if more resources and effort have been expended for high-level sports in these countries, their performance in the medal counts would not be too surprising. However, the evidence found after the collapse of the German Democratic Republic suggests that systematic doping and doping research did exist at least in that socialist country.

(27.) Summarizing, the game-theoretic models that have been developed recently to explain the (seemingly widespread) use of doping (thus mainly addressing Questions 2 and 3 given above) differ in a number of assumptions: first, are contestants homogenous with regards to their abilities and the degree of risk-aversion or are they heterogeneous? Second, do contestants move simultaneously or sequentially? Third, do contestants benefit from doping to the same extent or do they react differently to the consumption of banned substances?

(28.) A simple, yet unrealistic solution to the doping problem is to reduce the amounts of money that can be earned by the most successful athletes: with less money at stake, the incentives to use illegal drugs would be considerably reduced at least for athletes who have exit options that are acceptable to them. For athletes without exit options, that is, particularly those from underdeveloped countries whose second-best alternative is unemployment, such a reduction would also lead to a change in behavior: if the number of contestants goes down, the incentives to use illegal drugs go down too.

(29.) Awarding additional prizes to those finishing, for example, second and third in a tournament has been shown to positively influenec effort levels by all participants (cf. Valletti and Szymanski, 2005). This may also help reduce cheating by avoiding a "winner-take-all contest."

(30.) This approach may be ethically questionable because it relies on suspicion and informing, contrary to fair play, like doping itself. It is also based on the assumption that the loser has better knowledge of doping by the winner than third parties.

* We are grateful to two anonymous referees, whose comments have considerably improved the article. Any remaining errors and omissions are, of course, our own.

Dilger: Professor, Institute for Economic Education and Centrum for Management, University of Munster. Scharnhorststr. 100, D-48151 Munster, North Rhine-Westphalia, Germany. Phone +49-251-83-25330, Fax +49-251-3-28429, E-mail alexander.dilger@ uni-muenster.de

Frick: Professor, Department of Management, University of Paderborn, Warburger Str. 100. D-33098 Paderborn, North Rhine-Westphalia. Phone +49-5251-60-2097, Fax +49-5251-60-3242, E-mail bernd.frick@notes.unipaderborn.de, and Institute for Labour Law and Industrial Relations in the European Community, University of Trier, D-54286 Trier, Rhineland-Palatinate, Germany. E-mail bfrick@uni-wh.de

Tolsdorf: Research Assistant, Faculty of Management and Economics, Witten/Herdecke University, Alfred-Herrhausen-Strasse 50, D-58448 Witten, North Rhine-Westphalia, Germany. Phone +49-2302-926-564, Fax +49-2303-926-587, E-mail frank.tolsdorf@uni-wh.de
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