THE EFFECT OF GATE REVENUE SHARING ON SOCIAL WELFARE

This paper provides a theoretical model of a team sports league based on contest theory and studies the welfare effect of gate revenue sharing. It derives two counterintuitive results. First, it challenges the "invariance proposition" by showing that revenue sharing reduces competitive balance and thus produces a more unbalanced league. Second, the paper concludes that a lower degree of competitive balance compared with the noncooperative league equilibrium yields a higher level of social welfare and club profits. Combining both results, it concludes that gate revenue sharing increases social welfare and club profits in our model. ( JEL L83)     

Total effort, competitive balance and the optimal contest success function

This paper shows that, in the constrained case, the value weighted contest success function (CSF) maximizes not only total effort, but every objective function which is increasing in total effort and competitive balance. In the unconstrained case, a first price all-pay auction with a reserve price is optimal only if the impact of competitive balance on the objective is small. Otherwise, a modified value weighted CSF is optimal.     

OVERINVESTMENT IN TEAM SPORTS LEAGUES: A CONTEST THEORY MODEL

This paper applies contest theory to provide an integrated framework of a team sports league and analyzes the competitive interaction between clubs. We show that dissipation of the league revenue arises from 'overinvestment' in playing talent as a direct consequence of the ruinous competitive interaction between clubs. This overinvestment problem increases if the discriminatory power of the contest function increases, revenue-sharing decreases, and the size of an additional exogenous prize increases. We further show that clubs invest more when they play in an open league compared with a closed league. Moreover, the overinvestment problem within open leagues increases with the revenue differential between leagues.     

Endogenous contest success functions: a mechanism design approach

We describe optimal contest success functions (CSF) which maximize expected revenues of an administrator who allocates under informational asymmetry a source of rent among competing bidders. It is shown that in the case of independent private values rent administrator’s optimal mechanism can always be implemented via some CSFs as posited by Tullock. Optimal endogenous CSFs have properties which are often assumed a priori as plausible features of rent-seeking contests; the paper therefore validates such assumptions for a broad class of contests. Various extensions or optimal CSFs are analyzed.     

REVENUE SHARING IN PROFESSIONAL SPORTS LEAGUES

We employ a model of n heterogenous profit-maximizing clubs to analyze the impact of revenue sharing in professional sports leagues on competitive balance. Revenues of each club depend on absolute quality, relative quality and on competitive balance itself so that our model captures much of the preceding literature as special cases. We show that revenue sharing always increases competitive balance if clubs differ only with respect to the impact of absolute quality on revenues. On the contrary, revenue sharing reduces competitive balance if only clubs' relative qualities play a role for revenues or if only two teams are considered.     

Foundations for contest success functions

In the literature, the outcome of contests is either interpreted as win probabilities or as shares of the prize. With this in mind, we examine two approaches to contest success functions (CSFs). In the first, we analyze the implications of contestants’ incomplete information concerning the ‘type’ of the contest administrator. While in the case of two contestants this approach can rationalize prominent CSFs, we show that it runs into difficulties when there are more agents. Our second approach interprets CSFs as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular CSFs and guidelines for the definition of new ones.

“The strategic approach also seeks to combine axiomatic cooperative solutions and non-cooperative solutions. Roger Myerson recently named this task the ‘Nash program’.”(Rubinstein 1985, p. 1151)

     

Generalized contest success functions

The key element of models of contest is the contest success function (CSF) which specifies the winning probabilities of agents. The existing axiomatizations of CSFs assume that contestants can make only one type of investment. This paper generalizes these axiomatizations to the case where each agent can have multiple types of investments. This allows us to provide a unified framework to extend and interpret the results of Skaperdas (Econ Theory 7:283–290, 1996) and Clark and Riis (Econ Theory 11:201–204, 1998), and rationalize some seemingly ad hoc CSFs used by applied researchers. This paper has benefitted from the comments of Aicke Hinrichs, Rene Levinsky, and two anonymous referees. We are especially thankful to one of the referees for detailed comments which have helped improve every aspect of this paper.     

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.     

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).     

Competitive balance in football leagues when teams have different goals

In the standard two-team model of professional league sports it is shown that if teams have different objectives (the maximization of, respectively, wins and profits) the competitive balance conditions get worse with respect to the case when teams share the same goal. A similar, though less clear-cut, result obtains in the three-team setup. These outcomes call for policy measures to restore the balance. Three such measures are examined here: market-size-based revenue sharing, general salary cap and team-specific salary cap. It is shown that, contrary to the same-goal-for-all case, each of them may bring more intra-league competition. A ranking of the three measures is also suggested.     

Rule changes and competitive balance in Formula One motor racing

This article provides an economic explanation of the frequent rule changes in the Formula One (F1) motor racing series. In a two-stage model, the FIA (the organizer of the F1) first decides whether to change the rules or not, and then the racing teams compete in a contest. It turns out that a rule change reduces the teams’ performances, but also improves competitive balance between the teams. The rule change is implemented, if the FIA's revenue gain from the latter effect overcompensates the FIA's revenue loss from the former effect. We provide empirical evidence from F1 seasons in the period 1950 to 2005, which supports the main implications of the model.     

Risk taking under heterogenous revenue sharing

We examine the impact of informal risk sharing on risk taking incentives when transfers are organized through a social network. A bilateral partial sharing rule satisfies that neighbors share equally a part of their revenue. In such a society, correlated technologies generate interdependent risk levels. We obtain three findings. First, there is a unique and interior Nash-equilibrium risk profile, and it is in general differentiated and related to the Bonacich measure of the risk sharing network. Second, more revenue sharing enhances risk taking on average, although some agents may lower their risk level. Last, we find that under investment might often be observed.     

When less is more: Rationing and rent dissipation in stochastic contests

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

GATE REVENUE SHARING AND LUXURY TAXES IN PROFESSIONAL SPORTS

This paper examines the impact of gate revenue sharing and luxury taxes on professional sports leagues within the context of a less restrictive demand function than those used in prior models. In contrast to previous studies, the analysis finds that the increased sharing of revenues may enhance competitive balance. Consistent with other models, the analysis finds that player salaries will diminish as the percentage of shared gate receipts rises. The analysis also explores several variations of luxury taxes. All have the effect of lowering salaries. The impact on league balance depends on how the tax is implemented and on how its proceeds are distributed. As with salary caps, enforcement problems exist with the tax.     

全渠道供应链协同要素关系模型实证研究

新零售要求全渠道供应链的整合和优化,供应链协同有助于全渠道供应链一体化的实现。了解协同要素间关系有利于协同战略的制定与实施,是实现全渠道供应链协同的基础。在供应链管理相关理论研究基础上,构建研究模型,并提出研究假设。在实证研究的基础上,运用结构方程和分层回归的方法对模型和假设进行检验。结果表明,（1）协同收益与供应链协同正相关,分为财务收益和运营收益两部分。（2）收益共享与协同收益的财务收益和运营收益均正相关。（3）信息共享在收益共享与财务收益、收益共享与运营收益的影响过程中起中介作用。（4）契约精神在收益共享与信息共享关系中起调节作用。（5）契约精神在信息共享与财务收益的关系中没有调节作用,在信息共享与运营收益的关系中有调节作用。     

PROGRESSIVE TAXATION AS A MEANS FOR IMPROVING COMPETITIVE BALANCE

The existing instruments for improving the competitive balance within a sports league, such as revenue sharing, restrictions on free agency and salary caps, all have their shortcomings. In this paper, we show that a progressive sports tax, the revenues of which are not redistributed to smaller teams in the league, could be a better instrument. From the broader perspective of the theory of optimum taxation, this instrument may have advantages as well.     

基于收益共享契约的三级供应链如何应对突发事件

本文针对一个由供应商-制造商-零售商构成的三级供应链,在考虑随机性需求基础上,探讨突发事件对三级供应链的影响,同时改进了协调供应链的收益共享契约,使之能够应对突发事件。     

Demand disruption and coordination of supply chain via effort and revenue sharing

This article explores the equilibrium behaviour of a basic supplier–retailer distribution channel under demand disruption via effort and revenue sharing contract. This differs from the traditional supply chain coordination model. Firstly, demand is simultaneously affected by retail price and nonprice marketing effort from manufacturers and retailers. Secondly, when the demand is disrupted, this article considers disruptions in the market scale and price sensitivity coefficient. Thirdly, the supply chain coordination model is proposed via effort and revenue sharing contract. In this way, the manufacturer reduces the wholesale price as an incentive for the retailer to share revenue. Finally, the total supply chain profit is greater with contract than no contract. This also constitutes another incentive for the players to follow the effort and revenue sharing contract.     

Labour Markets in Professional Sports

Important elements of supply and demand are starkly observable in professional athletics. Demand affects how pay varies with personal productivity, racial discrimination, the nature of factor substitutions, and player mobility. Property rights affect the supply of athletic talent, arms races and incentives to restrict competition. In sports, excess incentives to win can create negative externalities. Collective agreements such as reverse-order drafts, payroll caps and revenue sharing constrain these forces, but redistribute rents from talented players to owners because they punish success. The European approach–promoting better-performing teams and relegating those with the poorest records–punish failure.     

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.