相关论文: When neither team wants to win: a flaw of recent U…

For every sports tournament, it is an important requirement to provide contestants with the appropriate incentives to perform. However, incentive compatibility is usually considered an all or nothing (binary) concept in the academic…

Multi-stage tournaments consisting of a round-robin group stage followed by a knockout phase are ubiquitous in sports. However, this format is incentive incompatible if at least two teams from a group advance to the knockout stage where the…

Tournament organisers supposedly design rules such that a team cannot be strictly better off by exerting a lower effort. However, the European qualification tournaments for recent FIFA soccer World Cups are known to violate this…

The integrity of a sport can be seriously undermined if its rules punish winning as this creates incentives for strategic manipulation. Therefore, a sports tournament can be called unfair if the overall win probabilities are not ordered…

The outcome of some football matches has benefited both teams at the expense of a third team because head-to-head results were used for breaking ties. Inspired by these examples, our mathematical analysis identifies all possible collusion…

If the final position of a team is already secured independently of the outcomes of the remaining games in a round-robin tournament, it might play with little enthusiasm. This is detrimental to attendance and can inspire collusion and…

UEFA European Championship 1996 qualification is known to violate strategy-proofness. It has been proved recently that a team could be better off by exerting a lower effort: it might be optimal to concede some goals in order to achieve a…

One of the most serious violations of fairness in sports is when a team has clear incentives to lose a match, which hurt a third, innocent team. This is shown to be not only a theoretical possibility as the recently identified incentive…

We analyse a mathematical model of seeding for sports contests with round-robin qualifying tournaments. The standard seeding system based on coefficients measuring the historical performance of the teams is shown to be unfair as it might…

In the last round of the FIFA World Cup group stage, games for which the outcome does not affect the selection of the qualified teams are played with little enthusiasm. Furthermore, a team that has already qualified may take into account…

Fairness has several interpretations in sports, one of them being that the rules should guarantee incentive compatibility, namely, a team cannot be worse off due to better results in any feasible scenario. The current seeding regime of the…

According to recent empirical studies, the group draw of major sports tournaments can imply a high level of uncertainty, and some lucky teams enjoy an unfair advantage over the other teams. We propose a novel technique to quantify this draw…

UEFA declares that it is committed to respecting the fundamental values of sports. However, the qualification rules of the post-2024 UEFA Champions League are shown to be unfair: a game with misaligned incentives was narrowly avoided in the…

The paper discusses the strategy-proofness of sports tournaments with multiple group stages, where the results of matches already played in the previous round against teams in the same group are carried over. These tournaments, widely used…

In a round-robin tournament, a team may lack the incentive to win if its final rank does not depend on the outcome of the matches still to be played. This paper introduces a classification scheme to determine these weakly (where one team is…

The paper analyses how draw constraints influence the outcome of a knockout tournament. The research question is inspired by European club football competitions, where the organiser generally imposes an association constraint in the first…

The Union of European Football Associations (UEFA) distributes commercial revenue from its club competitions according to a complex mechanism. Coefficient-based amounts are paid such that the participating teams are ranked on the basis of…

The paper investigates the qualification for the UEFA Champions League, the most prestigious club competition in European football with respect to the theoretical property of strategy-proofness. We find that in three seasons (2015-16,…

Many recent proposals for reducing tanking in draft lotteries share a common structure: losses improve draft position early in the season while wins improve draft position later. While such systems improve late-season incentives, they…

The draw of some knockout tournaments requires finding a perfect matching in a balanced bipartite graph. The problem becomes challenging with draw constraints: the two draw procedures used in sports are known to be non-uniformly distributed…