Knockout Tournament Design

Knockout Tournament Design PDF

Author: Thuc Duy Vu

Publisher: Stanford University

Published: 2010

Total Pages: 104

ISBN-13:

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Knockout tournaments constitute a very common and important form of social institution. They are perhaps best known in sporting competitions, but also play a key role in other social and commercial settings as they model a specific type of election scheme (namely, sequential pairwise elimination election). In such tournaments the organizer controls the shape of the tournament (a binary tree) and the seeding of the players (their assignment to the tree leaves). A tournament can involve millions of people and billions of dollars, and yet there is no consensus on how it should be organized. It is usually dependent on arbitrary decisions of the organizers, and it remains unclear why one design receives precedence over another. The question turns out to be surprisingly subtle. It depends among other things on (a) the objective, (b) the model of the players, (c) the constraints on the structure of the tournament, and (d) whether one considers only ordinal solutions or also cardinal ones. We investigate the problem of finding a good or optimal tournament design across various settings. We first focus on the problem of tournament schedule control, i.e., designing a tournament that maximizes the winning probability of a target player. While the complexity of the general problem is still unknown, various constraints -- all naturally occurring in practice -- serve to push the problem to one side or the other: easy (polynomial) or hard (NP-complete). We then address the question of how to find a fair tournament. We consider two alternative fairness criteria, adapted from the literature: envy-freeness and order preservation. For each setting, we provide either impossibility results or algorithms (either exact or heuristic) to find such a fair tournament. We show through experiments that our heuristics are both efficient and effective. Finally, using a combination of analytic and experimental tools we investigate the optimality of ordinal solutions for three objective functions: maximizing the predictive power, maximizing the expected value of the winner, and maximizing the revenue of the tournament. The analysis relies on innovative upper bounds that allow us to evaluate the optimality of any seeding, even when the number of possible seedings is extremely large.

Knockout Tournament Design

Knockout Tournament Design PDF

Author: Thuc Duy Vu

Publisher:

Published: 2010

Total Pages:

ISBN-13:

DOWNLOAD EBOOK →

Knockout tournaments constitute a very common and important form of social institution. They are perhaps best known in sporting competitions, but also play a key role in other social and commercial settings as they model a specific type of election scheme (namely, sequential pairwise elimination election). In such tournaments the organizer controls the shape of the tournament (a binary tree) and the seeding of the players (their assignment to the tree leaves). A tournament can involve millions of people and billions of dollars, and yet there is no consensus on how it should be organized. It is usually dependent on arbitrary decisions of the organizers, and it remains unclear why one design receives precedence over another. The question turns out to be surprisingly subtle. It depends among other things on (a) the objective, (b) the model of the players, (c) the constraints on the structure of the tournament, and (d) whether one considers only ordinal solutions or also cardinal ones. We investigate the problem of finding a good or optimal tournament design across various settings. We first focus on the problem of tournament schedule control, i.e., designing a tournament that maximizes the winning probability of a target player. While the complexity of the general problem is still unknown, various constraints -- all naturally occurring in practice -- serve to push the problem to one side or the other: easy (polynomial) or hard (NP-complete). We then address the question of how to find a fair tournament. We consider two alternative fairness criteria, adapted from the literature: envy-freeness and order preservation. For each setting, we provide either impossibility results or algorithms (either exact or heuristic) to find such a fair tournament. We show through experiments that our heuristics are both efficient and effective. Finally, using a combination of analytic and experimental tools we investigate the optimality of ordinal solutions for three objective functions: maximizing the predictive power, maximizing the expected value of the winner, and maximizing the revenue of the tournament. The analysis relies on innovative upper bounds that allow us to evaluate the optimality of any seeding, even when the number of possible seedings is extremely large.

Tournament Design

Tournament Design PDF

Author: László Csató

Publisher: Springer Nature

Published: 2021-01-04

Total Pages: 172

ISBN-13: 3030598446

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This Palgrave Pivot presents tournament design mainly within the axioms of incentive compatibility and fairness. It illustrates the advantages of an axiomatic approach through various examples, including several FIFA and UEFA tournaments, and uses theoretical tools and simulation methodology in its analysis. Chapter 1 discusses scoring systems of championships with multiple competitions, ranking in Swiss-system tournaments, and tie-breaking rules in round-robin leagues. It is followed by a thorough critical analysis of the current and previous FIFA World Rankings. The broad focus is substantially narrowed in Chapter 2, which turns to the topic of incentive (in)compatibility in multiple qualifiers. It is revealed that UEFA has faced at least three times recently this problem in the qualification to the UEFA Europa League, qualification to the UEFA Champions League, and the draw of the UEFA Champions League groups. Analogously, Chapter 3 discusses incentive (in)compatibility when there is only one group-based tournament but the complex progression rules to the subsequent stage can be designed poorly. Our examples include the qualifying tournaments of recent FIFA World Cups and UEFA European Championships. Chapter 4 moves to the problem of penalty shootout rules in soccer, where the fairness and complexity of some alternative mechanisms from the literature are evaluated. Fairness remains the central issue in Chapter 5, which presents the challenges of designing a tournament with 24 teams if the number of teams per group cannot exceed four. As expected, there is no perfect solution, and both FIFA and UEFA have introduced a reform in this format recently. Chapter 6 deals with the qualification for the 2020 UEFA European Football Championship. Its tournament design is perhaps the most complicated one that has ever been implemented in the real-world and suffers from serious shortcomings.

Contest Theory

Contest Theory PDF

Author: Milan Vojnović

Publisher: Cambridge University Press

Published: 2016-02-04

Total Pages: 737

ISBN-13: 1316472906

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Contests are prevalent in many areas, including sports, rent seeking, patent races, innovation inducement, labor markets, scientific projects, crowdsourcing and other online services, and allocation of computer system resources. This book provides unified, comprehensive coverage of contest theory as developed in economics, computer science, and statistics, with a focus on online services applications, allowing professionals, researchers and students to learn about the underlying theoretical principles and to test them in practice. The book sets contest design in a game-theoretic framework that can be used to model a wide-range of problems and efficiency measures such as total and individual output and social welfare, and offers insight into how the structure of prizes relates to desired contest design objectives. Methods for rating the skills and ranking of players are presented, as are proportional allocation and similar allocation mechanisms, simultaneous contests, sharing utility of productive activities, sequential contests, and tournaments.

Combinatorial Models for Scheduling Sports Tournaments

Combinatorial Models for Scheduling Sports Tournaments PDF

Author: Celso C. Ribeiro

Publisher: Springer Nature

Published: 2023-11-04

Total Pages: 197

ISBN-13: 3031372832

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This book introduces solutions for sports scheduling problems in a variety of settings. In particular the book covers timetabling, the traveling tournament problem, carryover minimization, breaks minimization, tournament design, tournament planning, and referee assignment. A rich selection of applications to sports such as football, baseball, basketball, cricket or hockey are employed to illustrate the methods and techniques. In a step-by-step tutorial format the book describes the use of graph theory concepts, local search operators and integer programming in the context of sports scheduling. The methods presented in this book are essential to sports scheduling in all its dimensions, from tournaments that are followed by millions of people across the world, with broadcast rights that amount to hundreds of millions of dollars in some competitions, to amateur leagues that require coordination and logistical efforts due to the large number of tournaments and competitors.

International Handbook on the Economics of Mega Sporting Events

International Handbook on the Economics of Mega Sporting Events PDF

Author: Wolfgang Maennig

Publisher: Edward Elgar Publishing

Published: 2012

Total Pages: 641

ISBN-13: 0857930273

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From the Olympics to the World Cup, mega sporting events are a source of enjoyment for tens of thousands, but can also be a source of intense debate and controversy. This insightful new Handbook addresses a number of central questions, including: How are host cities selected and under what economic conditions? How are these events organized, and how is local resistance overcome? Based on historical and empirical experience, what are the pitfalls for the organizers of these events? What are the potential economic benefits, including any international image effects? How can the costs be minimized and the benefits maximized for host cities and countries? How do these mega events impact the challenges of globalization and what is their environmental legacy? Compiled and edited by two internationally renowned sports economists, the expert contributions elaborate on the specific mechanisms of the bid processes, analyse the determining factors of winning bids, and illustrate how to construct future bid campaigns. Underpinned by case studies from four continents and by theoretical considerations, the reasons for seemingly systemic cost overruns are explored and analysed, as are the effects on national and regional employment and income, property values, non-traditional economic variables (such as psychological and marketing benefits) and urban branding and transformation. The Handbook also reflects on important elements of design of the games in order to better plan, prepare and allocate resources – including, for example, sustainability issues and the use of campaigns to secure positive perceptions. This book provides an up-to-date analysis of the financing and economic impact of mega sporting events, as well as a full discussion of how host cities can maximize the benefits from their experience. As such, it will prove a fascinating read for academics, students, researchers and policymakers with an interest in economics and public sector economics generally, and more specifically, in the economics of sport.

Routledge Handbook of Football Business and Management

Routledge Handbook of Football Business and Management PDF

Author: Simon Chadwick

Publisher: Routledge

Published: 2018-11-19

Total Pages: 624

ISBN-13: 1351262785

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Soccer is the world’s most valuable sport, generating bigger revenues, as well as being watched and played by more people, than any other. It is virtually impossible to understand the business of sport without understanding the football industry. This book surveys contemporary football in unparalleled breadth and depth. Presenting critical insights from world-leading football scholars and introducing football’s key organisations, leagues and emerging nations, it explores key themes from governance and law to strategy and finance, as well as cutting edge topics such as analytics, digital media and the women’s game. This is essential reading for all students, researchers and practitioners working in football, sport business, sport management or mainstream business and management.

High-Performance Communication Networks

High-Performance Communication Networks PDF

Author: Jean Walrand

Publisher: Elsevier

Published: 1999-10-25

Total Pages: 716

ISBN-13: 0080508030

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By focusing on the convergence of the telephone, computer networking, cable TV, and wireless industries, this fully revised second edition explains current and emerging networking technologies. The authors proceed from fundamental principles to develop a comprehensive understanding of network architectures, protocols, control, performance, and economics. Communications engineers, computer scientists, and network administrators and managers will appreciate the book for its perspectives on the innovations that impact their work. Students will be enriched by the descriptive and thorough coverage of networking, giving them the knowledge to explore rewarding career opportunities. * Provides the most recent information on * wide and local area networks, including WDM and optical networks, Fast and Gigabit Ethernets* access networks, such as cable modems and DSL;* approaches for quality-differentiated services in IP and ATM networks.* Examines the Internet, including proposed advances for improved performance and quality of service.* Presents a comprehensive discussion of wireless networks for voice and data.* Explains the economic factors and technical tradeoffs that guide network development.* Derives (in self-contained sections) the most important mathematical results of network performance

Twenty Lectures on Algorithmic Game Theory

Twenty Lectures on Algorithmic Game Theory PDF

Author: Tim Roughgarden

Publisher: Cambridge University Press

Published: 2016-08-30

Total Pages: 356

ISBN-13: 1316781178

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Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.

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