Our fans in the north: the demand for British Rugby League

This paper reports the results of estimating a single equation model of an attendance function for British Rugby League over the seasons 1982/83 to 1990/91. The data are panel data covering virtually every team which played in the two division league over the nine year time period. Diagnostic tests indicate that the appropriate model is a semilog random effects model, where the dependent variable is league attendance weighted by population. The major results are as follows: there are significant positive relationships between league attendance and various measures of team success (although the direction of causality is moot), team quality (as proxied by the two divisions) and the economic quality of team location (as proxied by the unemployment rate); but there is no discernible relationship between league attendance and either success in nonleague trophy competitions or measures of exceptional player quality.     

Racial Discrimination in English football

This paper examines data on the racial composition and financial and sporting performance of professional English soccer teams between 1974 and 1993. In an earlier paper, Szymanski showed that teams with an above average proportion of black players would tend to perform better on average that would have been expected given the aggregate wage bills of these clubs. Since players are more or less freely traded in soccer this presents strong market‐based evidence of discrimination. In the present paper we explore the source of such discrimination. In particular we are concerned to test the hypothesis that discrimination is attributable to the fans rather than the owners. If fans were racially prejudiced then the owners of a team might expect to generate a smaller marginal revenue product from a black player compared to an equally skilled white player. We assess the presence of fan discrimination by examining relationships between attendance, revenues, performance and the proportion of black players in the team. We also incorporate evidence regarding statements of racial prejudice (from the British Social Attitudes Survey) in particular regions. We find little evidence that the discrimination against black players has its source in fan discrimination.     

The Race that Stops a Nation: The Demand for the Melbourne Cup

This article uses the bounds testing procedure to cointegration, within an autoregressive distributed lag framework to estimate the determinants of attendance at the Melbourne Cup from its inception from 1861 to 2002. Following the literature on the demand for professional team sports, attendance is specified as a function of economic, demographic and race-specific factors. The main findings are that real income and population size are the major determinants of attendance in the long run, while in the short run the weather is the most important factor explaining attendance.     

The demand for standing and seated viewing accommodation in the English Football League

Using match attendance data collected from a postal survey of Football League clubs, separate demand equations are estimated for standing and seated viewing accommodation. Some significant differences between attendance patterns for the two types of accommodation are identified: current form, the championship significance of the match and a geographical distance variable are found to be important determinants of standing attendance, while the club's historical record is of particular importance for seated attendance. The paper also discusses the implications of the results in view of the current moves towards the conversion of stadia to all-seated accommodation.     

Attendance and pricing at sporting events: empirical results from Granger Causality Tests for the Melbourne Cup

This study applies Granger causality tests to examine the relationship between attendance, admission prices and real income at the Melbourne Cup, which is Australia’s premier horseracing event and one of the world’s leading handicap races. The motivation for the paper is that while market demand suggests that causation should run from admission price to attendance, it is equally plausible that sporting authorities could alter admission prices in response to a change in demand reflected in attendance. The main findings are that in the short-run there is unidirectional Granger causality running from income to attendance, attendance to admission price and income to admission price, while in the long run both admission price and income Granger cause attendance.     

On the convergence to the Nash bargaining solution for action-dependent bargaining protocols

We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player. We consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized. Otherwise, equilibrium proposals of all players converge to a weighted Nash bargaining solution, where the weights are determined by the probability to propose conditional on one's own rejection.     

Fighting as a profit maximizing strategy in the National Hockey League: more evidence

This article estimates the effect of fighting in hockey games on attendance in the National Hockey League (NHL) over the 1997–1998 through 2009–2010 seasons. After estimating a system of equations developed from a model of a profit-maximizing club owner, it was found that fighting had a small negative effect on attendance implying that encouraging fighting on the ice is not a profit-maximizing strategy. The results are quite robust when incorporating capacity constraints on attendance and exogenous ticket pricing. Other factors that determine club performance and market size were found to significantly affect attendance. The empirical results also suggest that NHL club owners are maximizing profit.     

Sport event attendance as a function of education: evidence from the UK

This article studies the role of education in the decision to attend sporting events. The overall objective is to verify whether more educated individuals are more likely to go to sports events than their less educated counterparts. If education socializes persons to focus on sports, it would then partially offset negative alternatives such as alcohol, drug abuse and unlawful behaviours, creating a positive externality. Sport events consumption is extensive, highlighting the potential economic importance of the sports-education externality. To establish the role of education in sport attendance, this article applies a probabilistic linear regression model to data from the UK. The econometric formulation associates sport event attendance in the left hand side with education in the right hand side, while controlling for the socioeconomic variables that are known to affect a consumer’s decision to go to a sport event: gender, age, income, employment status, children, marital status, and geographical location, among others. These findings add to a somewhat limited literature on both the effect of education on sports attendance and secondarily, on the impact of other socioeconomic variables on attendance.     

Uncertainty of outcome versus reputation: Empirical evidence for the First German Football Division

This paper deals with the determinants of match attendance in the German premier football league. We analyse uncertainty measures of match outcome as well as uncertainty of championship outcome. Furthermore, we incorporate supporter clubs, reputation, performance measures and weather effects as explanatory variables. Due to the limited capacity of the stadiums, observations on attendance are right censored in our sample. While other authors use the ordinary least squares estimator, which is inconsistent in this framework, we take this restriction implicitly in consideration by using a Tobit model. In conclusion, we show that reputation and goodwill are more important for attendance levels than the thrill of outcome uncertainty.¹ First version received: September 1999/Final version received: January 2001     

Informational properties of the Nash solutions of two stochastic nonzero-sum games

Within the framework of stochastic two-person nonzero-sum games, we deal with two commonly used models in engineering and economics—namely, the LQG (Linear-Quadratic-Gaussian) and the duopoly problems. We investigate how variations in information available to either player affect the equilibrium Nash strategies for these two models, whose existence and uniqueness have been proven in the paper. We show that for the LQG model better information for either player results in lower average Nash costs for both players; whereas for the duopoly model better information for one player helps him alone to achieve a higher average Nash profit, and it hurts the other player in the sense that his average Nash profit decreases. We further relate these properties of the Nash solutions for these two games to some of the distinct features of zero-sum games and team problems.     

Non-cooperative bargaining in apex games and the kernel

This paper studies non-cooperative bargaining with random proposers in apex games. Two different protocols are considered: the egalitarian protocol, which selects each player to be the proposer with equal probability, and the proportional protocol, which selects each player with a probability proportional to his number of votes. Expected equilibrium payoffs coincide with the kernel for the grand coalition regardless of the protocol. The equilibrium is in mixed strategies and the indifference conditions can be reinterpreted in the language of the kernel.     

Learning to play games in extensive form by valuation

Game theoretic models of learning which are based on the strategic form of the game cannot explain learning in games with large extensive form. We study learning in such games by using valuation of moves. A valuation for a player is a numeric assessment of her moves that purports to reflect their desirability. We consider a myopic player, who chooses moves with the highest valuation. Each time the game is played, the player revises her valuation by assigning the payoff obtained in the play to each of the moves she has made. We show for a repeated win-lose game that if the player has a winning strategy in the stage game, there is almost surely a time after which she always wins. When a player has more than two payoffs, a more elaborate learning procedure is required. We consider one that associates with each move the average payoff in the rounds in which this move was made. When all players adopt this learning procedure, with some perturbations, then, with probability 1 there is a time after which strategies that are close to subgame perfect equilibrium are played. A single player who adopts this procedure can guarantee only her individually rational payoff.     

Characterization of the extreme core allocations of the assignment game

A characterization of the extreme core allocations of the assignment game is given in terms of the reduced marginal worth vectors. For each ordering in the player set, a payoff vector is defined where each player receives his or her marginal contribution to a certain reduced game played by his or her predecessors. This set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is proved to be the set of extreme points of the core of the assignment game. Therefore, although assignment games are hardly ever convex, the same characterization of extreme core allocations is valid for convex games.     

Tourism's contribution to the demand for London's lively arts

How much of the attendance at London's lively arts comes from tourism? This question steers the inquiry, which involves model that distinguishes resident demand from tourist demand. Data for the empirical work are time series on individual arts companies, and accordingly the estimation method allows for autocorrelation and heteroscedasticity. Estimation indicates that, consonant with time-allocation logic, tourist demand depends importantly upon income whereas resident demand does not. It is shown that tourists, whose arts participation rate averages only 8%, account for 65% of attendance and that the elasticity measuring the attendance response to tourism equals 0.645.

It must be concluded that if it were not for overseas visitors to London, it is doubtful whether West End theatres could remain open throughout the summer.

Society of West End Theatre (1982, pp. 6–7)     

Location and attendance in major league baseball

This study uses a travel-cost model to analyse the attendance impacts on Major League Baseball (MLB) of the closest substitute MLB team. It is found that the closer two teams are, the lower attendance is at each team relative to two teams that are farther apart. In addition, when a new team moves into the area of an existing team, there is an additional initial reduction in attendance for the incumbent team. This has implications for actions aimed at changing the number of teams in MLB either by contraction or by possible antitrust approaches that would increase the number of teams, especially in megalopolis markets. Further, and consistent with past demand studies, pricing is in the inelastic portion of gate demand and fan loyalty is a significant contributor to the estimation of gate attendance.     

Examining the reliability of self-reported data on school participation

Many studies evaluate the impacts of Conditional Cash Transfer (CCT) programs on schooling using self-reports on enrollment and attendance even though there are reasons to doubt the reliability of these data. In this paper, we examine the extent to which school-age girls overstate their school participation. Using administrative data from a cash transfer experiment in Malawi and school attendance ledgers collected as part of the impact evaluation, we find that while all study participants overstate their enrollment and attendance rates, the extent to which this happens is significantly higher in the control group than the CCT arm. This finding implies that exclusive reliance on self-reported school participation data can lead to a serious underestimation of actual program impacts. We recommend that self-reports be supplemented using alternative sources of data on school participation that are appropriate to the experiment at hand — even if such efforts are likely to increase evaluation costs.     

On the impossibility of achieving no regrets in repeated games

Regret-minimizing strategies for repeated games have been receiving increasing attention in the literature. These are simple adaptive behavior rules that lead to no regrets and, if followed by all players, exhibit nice convergence properties: the average play converges to correlated equilibrium, or even to Nash equilibrium in certain classes of games. However, the no-regret property relies on a strong assumption that each player treats her opponents as unresponsive and fully ignores the opponents’ possible reactions to her actions. We show that if at least one player is slightly responsive, it is impossible to achieve no regrets, and convergence results for regret minimization with responsive opponents are unknown.     

Finite automata play the repeated prisoner's dilemma

The paper studies two-person supergames. Each player is restricted to carry out his strategies by finite automata. A player's aim is to maximize his average payoff and subject to that, to minimize the number of states of his machine. A solution is defined as a pair of machines in which the choice of machine is optimal for each player at every stage of the game. Several properties of the solution are studied and are applied to the repeated prisoner's dilemma. In particular it is shown that cooperation cannot be the outcome of a solution of the infinitely repeated prisoner's dilemma.     

Are there too few trades during the NFL draft?

College football players are initially assigned to teams in the National Football League (NFL) through the league’s draft selection process. At each team’s turn to pick, the team has the option of exercising the pick itself or trading it to another team. If gains from trade are exhausted, draft picks should be exercised by the team with the highest expected value. That is, the expected player contribution garnered from a given pick should not be dependent on whether the pick was traded or retained. Regression results, however, indicate that controlling for a player’s draft position, when a team trades up to acquire a player, that player is more likely to have greater on-field success. This suggests that there are too few draft day trades. Plausible reasons are high transaction costs or the fear of media scrutiny that draft trades can engender.     

Dismissals and quits in repeated games

This paper studies repeated games, where player 1 can decide to let the opponent continue or replace her by a new player. We also allow for the possibility of player 2 quitting the game. When only layoffs can occur, a folk theorem for finite horizons obtains due to the threat that termination of the relationship imposes on player 2. However, quits limit this result to those cases in which the outside option for player 2 is small (lower than some Nash equilibrium payoff of the stage game).