How to design a multi-stage tournament when some results are carried over?

  title={How to design a multi-stage tournament when some results are carried over?},
  author={L'aszl'o Csat'o},
  journal={OR Spectrum},
  pages={683 - 707}
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 handball and other sports, are shown to be incentive incompatible in the sense that a team can be strictly better off by not exerting full effort in a game. Historical examples are presented when a team was ex ante disinterested in winning by a high margin… 

The unfairness of the revenue distribution system used in the UEFA club competitions

  • L'aszl'o Csat'o
  • Economics
    International Journal of Sport Policy and Politics
  • 2023
“ Given the objective function of the organizer and the technology of the auction/contest it is possible to design an optimal prize scheme contingent on the distribution of contestant

A double-elimination format for a 48-team FIFA World Cup

I present a double-elimination format for the 48-team FIFA World Cup ™ that solves many of the concerns raised about the considered formats with mixed round-robin with groups of 3 or 4 teams and

Minimising the risk of tanking in tournaments with a preliminary round-robin group stage

Multi-stage tournaments consisting of a round-robin group stage followed by a knockout phase are ubiquitous in sports. However, as has been verified recently, this format is incentive incompatible if

A paradox of tournament seeding

  • L'aszl'o Csat'o
  • Education
    International Journal of Sports Science & Coaching
  • 2022
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

Scholarly sports: Influence of social science academe on sports rules and policy

Abstract This paper is an orthogonal study to that of Kendall and Lenten (2017)—on the perverse unintended consequences of badly designed sports rules. This paper, unlike the previous one, focuses on



Incentives to lose revisited: The NHL and its tournament incentives

Can strategizing in round-robin subtournaments be avoided?

  • M. Pauly
  • Education
    Social Choice and Welfare
  • 2013
This paper develops a mathematical model of strategic manipulation in complex sports competition formats such as the soccer world cup or the Olympic games. Strategic manipulation refers here to the

When neither team wants to win: A flaw of recent UEFA qualification rules

It is shown that the root of the problem resides in the incentive incompatibility of certain UEFA qualification rules, and the governing bodies of major sports should choose strategy-proof tournament designs because of this.

Winning by Losing: Incentive Incompatibility in Multiple Qualifiers

It is demonstrated that the existing national rules of awarding places for the UEFA Champions Leagues and the UEFA Europa League, which are based on the results of the national championship, a round-robin tournament and the national cup, a knock-out tournament, might produce a situation where a team will be strictly better off by losing a game.

Strategic manipulation in tournament games

Losing to Win: Tournament Incentives in the National Basketball Association

The focus of tournament models has been rank‐order compensation schemes whereby participants receive higher payments for higher relative performance, either incrementally or winner‐takes‐all. Our

Tournament Incentives, League Policy, and NBA Team Performance Revisited

Taylor and Trogdon found evidence of shirking under some, but not all, draft lottery systems used in three different National Basketball Association (NBA) seasons. The authors use data from all NBA

Fair draws for group rounds in sport tournaments

Two draw systems for the group round of sport tournaments where there are some geographical and/or seeding restrictions are proposed and it is shown that the proposals are much better than the FIFA system and also outperform other recently developed systems.