# Tournaments, Fairness and the Prouhet‐Thue‐Morse Sequence

@article{PalaciosHuerta2012TournamentsFA, title={Tournaments, Fairness and the Prouhet‐Thue‐Morse Sequence}, author={Ignacio Palacios-Huerta}, journal={Macroeconomics: Consumption}, year={2012} }

The Prouhet‐Thue‐Morse sequence occurs as the answer to various apparently unrelated questions in combinatorics, differential geometry, number theory, physics, music, turtle graphics, and other areas in the natural sciences. This paper shows that it can also be the answer to an important question in economics: how should the order of a sequential tournament competition between two agents be determined to make it fair?

## 37 Citations

Thue, Combinatorics on words, and conjectures inspired by the Thue-Morse sequence

- Mathematics
- 2014

Nous d\'ecrivons quelques r\'esultats r\'ecents sur la suite de Thue-Morse, ainsi que des questions ou conjectures, dont l'une, due \`a Shevelev, est r\'esolue dans cet article.
We describe some…

Optimal tournament design: lessons from the men’s handball Champions League

- Economics
- 2020

This paper challenges the traditional seeding regime of round-robin tournaments that aims to create balanced groups. In particular, the design of the most prestigious European men’s handball club…

Overcoming the incentive incompatibility of tournaments with multiple group stages

- Education
- 2017

The paper discusses the strategy-proofness of sports tournaments with multiple group stages. This design divides the competitors into round-robin groups in the preliminary and main rounds. Some…

Designing Fair Tiebreak Mechanisms: The Case of FIFA Penalty Shootouts

- Economics
- 2015

This work designs sequentially fair shootout mechanisms such that in all symmetric Markov-perfect equilibria each of the skill-balanced teams has exactly 50% chance to win whenever the score is tied at any round.

Fairness in penalty shootouts: Is it worth using dynamic sequences?

- BusinessJournal of sports sciences
- 2022

Seven soccer penalty shootout rules that determine the kicking order are compared, from a theoretical perspective, in a reasonable model of First Mover Advantage to impact decisionmakers who can guarantee fairer outcomes in dynamic tournaments by a carefully chosen sequence of actions.

Ordering sequential competitions to reduce order relevance: Soccer penalty shootouts

- EconomicsPloS one
- 2020

This work model shootouts as a probability network, calibrate it using the data from the traditional ordering, and use the model to conduct counterfactual analysis which shows that alternating the team that shoots first in each round would reduce the impact of ordering.

A mathematical analysis of fairness in shootouts

- Computer Science
- 2020

It is shown that, for a sudden death, no repetitive sequence can be fair and the so-called Prohuet–Thue–Morse sequence is not fair, and an algorithm that outputs a fair sequence whenever one exists is found.

Take a Chance on Abba

- BiologySSRN Electronic Journal
- 2017

This study analyzes 1,701 men's and 920 women's tiebreak games from top-tier tournaments between the years 2012 to 2015 and finds that, for both genders, serving first does not have any significant effect on the winning probabilities of the two players, implying that the ABBA sequence is fair.

## References

SHOWING 1-10 OF 12 REFERENCES

The Ubiquitous Prouhet-Thue-Morse Sequence

- Computer Science, BiologySETA
- 1998

The Prouhet-Thue-Morse sequence appears to be somewhat ubiquitous, and it is described many of its apparently unrelated occurrences.

Psychological Pressure in Competitive Environments: Evidence from a Randomized Natural Experiment

- Economics
- 2008

Much like cognitive abilities, emotional skills can have major effects on perfor mance and economic outcomes. This paper studies the behavior of professional subjects involved in a dynamic…

Rank-Order Tournaments as Optimum Labor Contracts

- EconomicsJournal of Political Economy
- 1981

This paper analyzes compensation schemes which pay according to an individual's ordinal rank in an organization rather than his output level. When workers are risk neutral, it is shown that wages…

Increasing Dominance with No Efficiency Effect

- EconomicsJ. Econ. Theory
- 2002

It is shown that the laggard has an incentive to chose a different path from the leader, and the strategic choice of covariance in races results in a new force towards increasing dominance.

R&D Competition when firms Choose Variance

- Economics
- 2003

I consider an infinite-period race where players choose between low- and high-variance motion technologies. I provide sufficient conditions under which, in equilibrium, the leader chooses a safe…

Investment Under Uncertainty.

- Economics
- 1994

How should firms decide whether and when to invest in new capital equipment, additions to their workforce, or the development of new products? Why have traditional economic models of investment…

The Provision of Incentives in Firms

- Economics
- 1999

This paper provides an overview of the existing theoretical and empirical work on the provision of incentives. It reviews the costs and benefits of many types of pay-for-performance, such as piece…

Recurrent geodesics on a surface of negative curvature

- Mathematics
- 1921

The results necessary for the development of this paper are contained in a paper by G. D. Birkhoff,t in a paper by J. Hadamard.J and in an earlier paper by the present writer. § In this earlier…

Cognition and Emotion: Evidence from a Natural Experiment.

- Mimeo, LSE and Universidad de Santiago de Compostela,
- 2011