Some comparative economics of the organization of sports: competition and regulation in north American vs. European professional team sports leagues

This article contends that a new research avenue is open to comparative economics which is the economic comparison between American (closed) and European (open) professional team sports leagues. It starts with sketching the major institutional differences between the two leagues systems. Then it surveys the American modelling of competitive balance in these sports leagues that objects pro-competitive balance regulation as being non Walrasian when (American) teams are profit maximising. A next step is to cover how the Walrasian model has been adapted to European open leagues and their regulation of win maximising clubs under a hard budget constraint. Such approach has recently been outdated by models where win maximising clubs operate with a flexible supply of talent in a non cooperative game, given the globalization of the labour market for sporting talent (namely after the Bosman case). Finally, the article ploughs into a new research path advocating for a disequilibrium model where clubs would have a "soft" budget constraint rooted in their weak governance, and empirically tests a vicious circle between TV rights revenues and wages in French football that may explain the aforementioned disequilibrium.sports economics, comparative economics, economic organisation, governance, sports leagues, Walrasian model, Nash equilibrium, competitive balance, regulation, soft budget constraint, TV rights, wages, profit maximising, win maximising

Contest Theory and its Applications in Sports

This paper outlines how the theory of contests is applied to professional team sports leagues. In the first part, we present the traditional Tullock contest and explain some basic properties of the equilibrium. We will then extend this static contest to a two-period model in order to analyze dynamic aspects of contests. In the second part, we will present applications of contest theory in sports. In particular, we will show how the Tullock framework is applied to models of team sports leagues. For this purpose, we will first explain the value creation process in team sports leagues and show how club revenues are related to the contest success function. Then, we present some basic modeling issues; for instance, we show how the assumption of flexible vs. fixed talent supply depends on the league under consideration and how it influences the equilibria. Furthermore, we explicate the effect of revenue sharing on competitive balance in the different models. Then we address the relationship between competitive balance and social welfare. Finally, we illustrate why many clubs tend to "overinvest" in playing talent in many team sports leagues.Contest theory, Tullock contest, sports leagues, competitive balance, revenue sharing, social welfare, overinvestment

Doubts and equilibria

In real life strategic interactions decision-makers are likely to entertain doubts about the degree of optimality of their play. To capture this feature of real choice-making, we present here a model based on the doubts felt by an agent about how well is playing a game. The doubts are coupled with (and mutually reinforced by) imperfect discrimination capacity, which we model here by means of similarity relations. We assume that each agent builds procedural preferences defined on the space of expected payoffsstrategy frequencies attached to his current strategy. These preferences, together with an adaptive learning process lead to doubt-based selection dynamic systems. We introduce the concepts of Mixed Strategy Doubt Equilibria, Mixed Strategy Doubt-Full Equilibria and Mixed Strategy Doubtless Equilibria and show the theoretical and the empirical relevance of these concept

Do soccer players play the mixed-strategy Nash equilibrium?

Mixed-strategy Nash equilibrium (MSNE) is a commonly-used solution concept in game-theoretic models in various fields in economics, management, and other disciplines, but the experimental results whether the MSNE predicts well actual play in games is mixed. Consequently, evidence for naturally-occurring games in which the MSNE predicts the outcome well is of great importance, as it can justify the vast use of MSNE in models. The game between the kicker and goalkeeper in soccer penalty kicks is a real-world game that can be used to examine the application of the MSNE concept or its accuracy because payoffs are a common knowledge, the players have huge incentives to play correctly, the game is simple enough to analyze, its Nash equilibrium is in mixed strategies, and players' actions can be observed. We collected and analyzed data on the direction of kicks and jumps in penalty kicks in various top leagues and tournaments. Our analysis suggests that the MSNE predictions are the closest to the actual sample data, even though some other prediction methods use information on the marginal distribution of kicks or jumps whereas the MSNE does not.Soccer; Football; MSNE; Mixed-strategies; Mixed-strategy Nash equilibrium; Sports; Penalty kicks

Teaching Mixed Strategy Nash Equilibrium to Undergraduates

The authors present a simple and effective method for improving student comprehension of mixed strategies. After reviewing available texts, and with some trial and error, we feel that this method eases the teaching of the information and increases the students' ability to understand and retain concepts. Through a simple alteration to the normal form of a game, students can clearly see the results of employing mixed strategies, practise calculating expected payoffs, visualise the accompanying 'indifference' in the payoffs, and recognise the mixed strategy Nash equilibrium in a familiar way.

Bargaining with Non-Monolithic Players

This paper analyses strategic bargaining in negotiations between non-monolithic players, i.e. agents starting negotiations can split up in smaller entities during the bargaining process. We show that the possibility of scission in the informed coalition implies that it loses its information advantages. We also show that when the possibility of a scission exists the uninformed player does not focus on his or her beliefs about the strength of the informed coalition but on the proportion of weak/strong players within this coalition. Finally, our results show that the possibility of a scission reduces the incentives for the leader to propose a high offer to ensure a global agreement. We apply this framework to international negotiations on global public goods and to wage negotiations.Strategic bargaining, Non-monolithic players, Scission, Noncooperative game-theory

Incentives and Outcomes in a Strategic Setting: The 3-Points-For-A-Win System in Soccer

We exploit a major structural change that has occurred in world soccer to study the impact of incentives on outcomes in a strategic setting. A game-theoretic model is developed that captures some essential strategic elements of soccer vis-à-vis the number of points awarded to a win. The observable implications of the model are tested using a large dataset that spans 30 years and 35 countries. The empirical results support the theoretical model and show that the 3-point system has led to a statistically significant increase in the expected number of goals and a decrease in the fractions of drawn matches.Association football; Nash equilibrium; panel data; strategic incentives; supermodularity; tournaments

Doubts and Equilibria

In real life strategic interactions, decision-makers are likely to entertain doubts about the degree of optimality of their play. To capture this feature of real choice-making, we present here a model based on the doubts felt by an agent about how well is playing a game. The doubts are coupled with (and mutually reinforced by) imperfect discrimination capacity, which we model here by means of similarity relations. We assume that each agent builds procedural preferences de ned on the space of expected payoffs-strategy frequencies attached to his current strategy. These preferences, together with an adaptive learning process lead to doubt-based selection dynamic systems. We introduce the concepts of Mixed Strategy Doubt Equilibria, Mixed Strategy Doubt-Full Equilibria and Mixed Strategy Doubtless Equilibria and show the theoretical and the empirical relevance of these concepts.