Contests where there is variation in the marginal productivity of effort

Summary. We provide a characterization of participants' behavior in a contest or tournament where the marginal productivity of effort varies across contestants and individual productivity is private information. We then consider the optimal design of such a contest. We first analyze contestant behavior for the usual type of contest, where the highest output wins. Abilities need not be independently distributed. We demonstrate that there is a unique symmetric equilibrium output function, that output is increasing in ability, and that marginal effort is increasing in ability, while effort decreases when the cost of effort increases. Next we consider the case where the highest output need not win, with independently distributed abilities. We analyze the contest designer's decisions in choosing contest rules optimal from her perspective. We show that the output produced, probability of winning, and contest designer's expected revenue are generally increasing in contestants' ability. We examine the relationship between the marginal cost of producing output and marginal utility per dollar of the net award for winning. Received: July 30, 1998; revised version: August 7, 2000     

Asymmetric information contests

We consider how asymmetries in information affect contest behavior. We find two effects drive behavior-risk and perceptions of an opponent's value. Our results also suggest that the more tractable one-sided asymmetric information contest might be sufficient to capture contest behavior under uncertainty. However, the efficiency of a contest is sensitive to asymmetric information and the distribution a players' values because players with relatively low values can have an increased probability of success. Thus, it is important (a) to account for information asymmetries to avoid biasing predicted efficiency, and (b) to recognize that this bias is unsystematic.     

Uncertain contest success function

In this article, contestants play with a certain probability in Contest A and with the complementary probability in Contest B. This situation is called contest uncertainty. In both contests, effort is additively distorted by a contest noise parameter which affects the sensitivity of the contest success function (CSF). In Contest A (B), this parameter is linearly added to (subtracted from) effort. We analyze the interaction of contest uncertainty and contest noise on contestant behavior and profit. For symmetric contestants, contest noise has an ambiguous effect on effort and profit. We show that more contest uncertainty can imply greater effort. Furthermore, an introduction of an infinitesimal degree of contest uncertainty can have a large impact on effort and profit. Based on the analysis, this article presents the contest organizer's incentive to manipulate the degree of uncertainty in the contest. For profit or effort maximization, the contest organizer should always eliminate any uncertainty. If contestants are asymmetric, more contest noise increases effort as well as competitive balance if both Contests A and B have the same probability of occurrence.     

LOBBYING CONTESTS WITH ENDOGENOUS POLICY PROPOSALS

Lobbyists choose what to lobby for. If they can precommit to certain policy proposals, their choice will have an influence on the behavior of opposing lobbyists. Hence lobbyists have an incentive to moderate their policy proposals in order to reduce the intensity of the lobbying contest. This logic has been explored in a number of recent papers. I reconsider the topic with a perfectly discriminating contest. With endogenous policy proposals, there is a subgame-perfect equilibrium where the proposals of the lobbyists coincide and maximize joint welfare; moreover, this equilibrium is the only one that survives repeated elimination of dominated strategies. Hence there is no rent dissipation at all. A politician trying to maximize lobbying expenditures would prefer an imperfectly discriminating contest.     

Revenue Sharing,Competitive Balance and the Contest Success Function

Abstract. This paper investigates revenue sharing in an asymmetric two‐teams contest model of a sports league with Nash behavior of team owners. The innovation of the analysis is that it focuses on the role of the contest success function (CSF). In case of an inelastic talent supply, revenue sharing turns out to worsen competitive balance regardless of the shape of the CSF. For the case of an elastic talent supply, in contrast, the effect of revenue sharing on competitive balance depends on the specification of the CSF. We fully characterize the class of CSFs for which revenue sharing leaves unaltered competitive balance and identify CSFs ensuring that revenue sharing renders the contest closer.     

Investment in the absence of property rights; the role of incumbency advantages

In many situations the individuals who can generate some output must enter a contest for appropriating this output. This paper analyses the investment incentives of such agents and the role of incumbency advantages in the contest. Depending on the advantages, an increase in the productivity of the investment can decrease or increase the amount of investment. The results are applied to autocrats’ investment behavior and job specific investment in organizations.     

Repeated Contests with Asymmetric Information

The same contestants often meet repeatedly in contests. Behavior in a contest potentially provides information with regard to one's type and can therefore influence the behavior of the opponents in later contests. This paper shows that if effort is observable, this can induce a ratchet effect in contests: high ability contestants sometimes put in little effort in an early round in order to make the opponents believe that they are of little ability. The effect reduces overall effort and increases equilibrium utility of the contestants when compared with two unrelated one-shot contests. It does, however, also introduce an allocative inefficiency since sometimes a contestant with a low valuation wins. The model assumes an imperfectly discriminating contest. In an extension I show that, qualitatively, results are similar in a perfectly discriminating contest (all pay auction).     

Maximum efforts in contests with asymmetric valuations

Efforts may be reduced when players with different valuations participate in a contest. This paper considers the problem of designing a contest to elicit maximum aggregate effort from players with asymmetric valuations. Optimal designs for different classes of contest technologies are computed and characterized. A value weighted contest is optimal in the concave case. In the unconstrained case, the optimal contest is equivalent to a first price all-pay auction with a reserve price. The optimal design discounts the effort of the high valuation player in order to induce him to compete vigorously.     

Higher cognitive ability is associated with lower entries in a p-beauty contest

“Beauty contests” are well-studied, dominance-solvable games that generate two interesting results. First, most behavior does not conform to the unique Nash equilibrium. Second, there is considerable unexplained heterogeneity in behavior. In this work, we explore the relationship between beauty contest behavior and cognitive ability. We find that subjects with high cognitive ability exhibit behavior that is closer to the Nash equilibrium.     

Building Trade Barriers and Knocking Them Down

This paper examines the dynamic behavior of trade protection and liberalization. Consistent with evidence on the development of trade policies, policy decisions are modeled as the outcome of a political contest between import-competing interests and exporters. Uncertainty about the success of political contests yields a dynamic equilibrium in which tariffs gradually increase over time. Eventually, increasing tariffs reduce profits in the exporting sector to such a degree that exporters enter the political arena and lobby actively against protection. Depending on the market characteristics, a political contest may generate a liberalization or a move toward autarky.     

Contests with Multi-tasking*

The standard contest model in which participants compete in a single dimension is well understood and documented. Multi‐dimension extensions are possible but are liable to increase the complexity of the contest structure, mitigating one of its main advantages: simplicity. In this paper we propose an extension in which competition ensues in several dimensions, and a competitor that wins a certain number of these is awarded a prize. The amount of information needed to run the contest is hence limited to the number of dimensions won by each player. We look at the design of this contest from the point of view of maximising effort in the contest (per dimension and totally), and show that there will be a tendency to run small contests with few dimensions. The standard Tullock model and its results are encompassed by our framework.     

Heterogeneous outside options in contests

This article describes a large number of contestants with high and low levels of talent who individually decide to enter a contest or take their heterogeneous outside options. We derive a critical condition for which only high types, only low types or both types participate in the contest. If a contest organizer is worried about the type participating in the contest, then he/she should provide a contest with low noise to attract high types. However, if a contest organizer's objective is to maximize the individual effort, he/she will not necessarily prefer to have the high types in the contest.     

Experimental comparison of multi-stage and one-stage contests

This article experimentally studies a two-stage elimination contest and compares its performance with a one-stage contest. Contrary to the theory, the two-stage contest generates higher revenue than the equivalent one-stage contest. There is significant over-dissipation in both stages of the two-stage contest and experience diminishes over-dissipation in the first stage but not in the second stage. Our experiment provides evidence that winning is a component in a subject's utility. A simple behavioral model that accounts for a non-monetary utility of winning can explain significant over-dissipation in both contests. It can also explain why the two-stage contest generates higher revenue than the equivalent one-stage contest.     

Designing an optimal contest

The paper brings a mechanism design perspective to the study of contests. We consider the problem of selecting a contest success function when the contest designer may also value the prize. We show that any equilibrium outcome that can be achieved by a concave increasing contest success function can be replicated by a linear contest success function. An expected utility maximizing designer should employ a linear homogeneous contest success function. We explicitly derive the optimal contest for a risk-neutral designer and present comparative statics results. Tullock's contest is optimal only when the designer's valuation for the prize is low.     

Endogenous entry in contests

We report the results of laboratory experiments on rent-seeking contests with endogenous participation. Theory predicts that (a) contest entry and rent-seeking expenditures increase with the size of the prize and (b) earnings are equalized between the contest and the outside option. While the directional predictions offered in (a) are supported in the data, the level predictions are not. Prediction (b) is not supported in the data: when the prize is large, contest participants earn more than the outside option. When the prize is small, contest participants earn less. Previous studies of gender and contest competition suggest that females should (a) not perform as well in the contest; and (b) enter at a lower rate. We find some support for (a) but not for (b). Women participate in the contest at the same rate as men.     

Momentum and betting market perceptions of momentum in college football

Past research has demonstrated that bettors believe positive momentum carries over from contest to contest. This article examines whether there is any empirical support for this belief by testing for the presence of across-contest momentum effects in college football. We characterize momentum in multiple fashions and after controlling for between-team heterogeneity find no evidence that systematic relationships exist between the degree of momentum a team enters a contest with and the outcome of that contest. From a wagering market perspective, this indicates that there is no statistically significant advantage to betting on teams perceived to possess positive momentum. Our results also suggest that the combination of the opening betting line set by odds makers and the subsequent market movement of that line does not systematically overreact to teams on streaks.     

多属性拍卖与研发竞赛的激励效应比较

采购方向两个潜在的供应商之一采购某种需要研发的创新性技术或产品,并采用多属性拍卖机制或研发竞赛机制来确定哪一个供应商最终能赢得合约。假设供应商是同质的和风险中性的、研发成本具有随机性,且采购方和供应商之间在研发成本上信息不对称,分别研究多属性拍卖机制和研发竞赛机制中供应商的质量决策,比较这两种机制的创新激励效应。结果发现:多属性拍卖机制中,理性的供应商都不会进行研发和参与投标;研发竞赛中奖励金额必须要足够大才能激发供应商的研发与竞赛参与意愿,此时研发竞赛机制要优于多属性拍卖机制。     

Quantity-cum-quality contests

Quality and quantity are very common features of production processes. People care about these two features and they tend to be connected. I consider a contest in which the quantity and quality of output are rewarded. The output in the quality contest plays a dual role. It counts in the quality contest but it is also converted into quantity-equivalent output to obtain total output in the quantity contest. This latter feature implies that the two contests are interlinked. I find that when the unit cost of producing quality is sufficiently high, then treating quality and quantity as the same has a disincentive effect on the production of quality. In contrast, when the unit cost of producing quality is sufficiently low, treating quality and quantity as the same has no disincentive effect on the production of quality. I also find an equilibrium in which no one exerts effort in the quantity contest. When there is a binding budget constraint on effort, I find that effort in the quantity contest is smaller relative to the unconstrained case but effort in the quality contest may remain unchanged.     

Effort maximization in asymmetric contest games with heterogeneous contestants

Contest rules are set up by administrators who frequently have discretionary power in specifying the details of these rules, i.e., they can bias the contest rules toward specific contestants in order to further their prime objective. We derive the optimal bias of the contest rule for a contest administrator, who is interested in maximizing the total efforts expended in the contest. The solution is obtained in closed form for a widely used class of n-person contest games. Setting the optimal bias has important implications: (i) there is never exclusion of strong players, instead there is (endogenously induced) inclusion of weak contestants; (ii) the contest administrator will optimally level the playing field by encouraging weak contestants, but he will not equalize the contestants’ chances unless they are identical; and (iii) at least three contestants will be active in equilibrium of the optimal contest, irrespective of heterogeneity.     

Lottery versus all-pay auction contests: A revenue dominance theorem

We allow a contest organizer to bias a contest in a discriminatory way; i.e., she can favor specific contestants by designing the contest rule in order to maximize total equilibrium effort (resp. revenue). The two predominant contest regimes are considered, all-pay auctions and lottery contests. For all-pay auctions the optimal bias is derived in closed form: It implies extreme competitive pressure among active contestants and low endogenous participation rates. Moreover, the exclusion principle advanced by Baye et al. (1993) becomes obsolete in this case. In contrast, the optimally biased lottery induces a higher number of actively participating contestants due to softer competition. Our main result regarding total revenue comparison under the optimal biases reveals that the all-pay auction revenue-dominates the lottery contest for all levels of heterogeneity among contestants. The incentive effect due to a strongly discriminating contest rule (all-pay auction) dominates the participation effect due to a weakly discriminating contest rule (lottery).