The Mathematics of Decisions, Elections, and Games
The Mathematics of Decisions, Elections, and Games

Author: Karl-Dieter Crisman

Publisher: American Mathematical Society

Published: 2014-08-29

Total Pages: 242

ISBN-13: 0821898663

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This volume contains the proceedings of two AMS Special Sessions on The Mathematics of Decisions, Elections, and Games, held January 4, 2012, in Boston, MA, and January 11-12, 2013, in San Diego, CA. Decision theory, voting theory, and game theory are three intertwined areas of mathematics that involve making optimal decisions under different contexts. Although these areas include their own mathematical results, much of the recent research in these areas involves developing and applying new perspectives from their intersection with other branches of mathematics, such as algebra, representation theory, combinatorics, convex geometry, dynamical systems, etc. The papers in this volume highlight and exploit the mathematical structure of decisions, elections, and games to model and to analyze problems from the social sciences.

Mathematical Analyses of Decisions, Voting and Games
Mathematical Analyses of Decisions, Voting and Games

Author: Michael A. Jones

Publisher: American Mathematical Society

Published: 2024-03-25

Total Pages: 210

ISBN-13: 1470469782

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This volume contains the proceedings of the virtual AMS Special Session on Mathematics of Decisions, Elections and Games, held on April 8, 2022. Decision theory, voting theory, and game theory are three related areas of mathematics that involve making optimal decisions in different contexts. While these three areas are distinct, much of the recent research in these fields borrows techniques from other branches of mathematics such as algebra, combinatorics, convex geometry, logic, representation theory, etc. The papers in this volume demonstrate how the mathematics of decisions, elections, and games can be used to analyze problems from the social sciences.

Chance, Strategy, and Choice
Chance, Strategy, and Choice

Author: Samuel B. Smith

Publisher: Cambridge University Press

Published: 2015-06-29

Total Pages: 393

ISBN-13: 1107084520

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Games and elections are fundamental activities in society with applications in economics, political science, and sociology. These topics offer familiar, current, and lively subjects for a course in mathematics. This classroom-tested textbook, primarily intended for a general education course in game theory at the freshman or sophomore level, provides an elementary treatment of games and elections. Starting with basics such as gambling, zero-sum and combinatorial games, Nash equilibria, social dilemmas, and fairness and impossibility theorems for elections, the text then goes further into the theory with accessible proofs of advanced topics such as the Sprague-Grundy theorem and Arrow's impossibility theorem. * Uses an integrative approach to probability, game, and social choice theory * Provides a gentle introduction to the logic of mathematical proof, thus equipping readers with the necessary tools for further mathematical studies * Contains numerous exercises and examples of varying levels of difficulty * Requires only a high school mathematical background.

Chaotic Elections!
Chaotic Elections!

Author: Donald Saari

Publisher: American Mathematical Soc.

Published: 2001-04-03

Total Pages: 178

ISBN-13: 9780821886168

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What does the 2000 U.S. presidential election have in common with selecting a textbook for a calculus course in your department? Was Ralph Nader's influence on the election of George W. Bush greater than the now-famous chads? In Chaotic Elections!, Don Saari analyzes these questions, placing them in the larger context of voting systems in general. His analysis shows that the fundamental problems with the 2000 presidential election are not with the courts, recounts, or defective ballots, but are caused by the very way Americans vote for president. This expository book shows how mathematics can help to identify and characterize a disturbingly large number of paradoxical situations that result from the choice of a voting procedure. Moreover, rather than being able to dismiss them as anomalies, the likelihood of a dubious election result is surprisingly large. These consequences indicate that election outcomes--whether for president, the site of the next Olympics, the chair of a university department, or a prize winner--can differ from what the voters really wanted. They show that by using an inadequate voting procedure, we can, inadvertently, choose badly. To add to the difficulties, it turns out that the mathematical structures of voting admit several strategic opportunities, which are described. Finally, mathematics also helps identify positive results: By using mathematical symmetries, we can identify what the phrase ``what the voters really want'' might mean and obtain a unique voting method that satisfies these conditions. Saari's book should be required reading for anyone who wants to understand not only what happened in the presidential election of 2000, but also how we can avoid similar problems from appearing anytime any group is making a choice using a voting procedure. Reading this book requires little more than high school mathematics and an interest in how the apparently simple situation of voting can lead to surprising paradoxes.

Mathematics and Democracy
Mathematics and Democracy

Author: Steven J. Brams

Publisher: Princeton University Press

Published: 2009-12-02

Total Pages: 390

ISBN-13: 1400835593

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Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In Mathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods more fairly. One of the procedures that Brams proposes is "approval voting," which allows voters to vote for as many candidates as they like or consider acceptable. There is no ranking, and the candidate with the most votes wins. The voter no longer has to consider whether a vote for a preferred but less popular candidate might be wasted. In the same vein, Brams puts forward new, more equitable procedures for resolving disputes over divisible and indivisible goods.

Coordinate Systems for Games
Coordinate Systems for Games

Author: Daniel T. Jessie

Publisher: Springer Nature

Published: 2019-12-13

Total Pages: 217

ISBN-13: 303035847X

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This monograph develops a method of creating convenient coordinate systems for game theory that will allow readers to more easily understand, analyze, and create games at various levels of complexity. By identifying the unique characterization of games that separates the individual’s strategic interests from the group’s collective behavior, the authors construct a single analytical methodology that readers will be able to apply to a wide variety of games. With its emphasis on practicality and approachability, readers will find this book an invaluable tool, and a viable alternative to the ad hoc analytical approach that has become customary for researchers utilizing game theory. The introductory chapters serve two important purposes: they review several games of fundamental importance, and also introduce a dynamic that is inherent in games, but has gone unexplored until now. After this has been established, readers will advance from simple 2 x 2 games to games with more player strategies and dynamics. For interested readers, a rigorous treatment of the underlying mathematics is conveniently gathered at the end of the book. Additional topics of interest, such as extensive form and coalitional games, are presented to help readers visualize more complex settings that will be vital in aiding the understanding of advanced topics, such as coalition-free Nash points, multi-player repeated games, and more. Coordinate Systems for Games is ideal for a wide variety of researchers interested in game theory, including social scientists, economists, mathematicians, computer scientists, and more. The authors' approachable style also makes this accessible to an audience at any scale of experience, from beginning non-specialists to more practiced researchers.

Strategic Decisions: The Mathematics of Game Theory
Strategic Decisions: The Mathematics of Game Theory

Author: Lexa N. Palmer

Publisher: Book Lovers HQ

Published: 2024-07-31

Total Pages: 195

ISBN-13:

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Embark on a journey to unlock the secrets behind successful decision-making with "Strategic Decisions: The Mathematics of Game Theory." This comprehensive exploration leaves no stone unturned in the intricate world of game theory, offering insights into how individuals, businesses, and nations make strategic choices in various contexts. Whether you're navigating the complexities of competitive markets, political landscapes, or everyday interactions, this book equips you with the tools to understand and influence outcomes, ensuring a confident and reassured learning journey. In "Strategic Decisions," you'll not only grasp the foundational game theory concepts, including Nash equilibrium, dominant strategies, and mixed strategies, but also witness their real-world applications. The book transcends theory to explore practical applications in economics, politics, business, and beyond, empowering you with the knowledge of how game theory can be applied to real-world situations. From optimizing market strategies to understanding the dynamics of international relations, this book provides a rich understanding of the strategic behavior that shapes our world. What You Will Find in This Book: The history and evolution of game theory Key concepts like Nash equilibrium and dominant strategies Applications of game theory in economics and market strategies Insights into political strategy and international relations The role of information and signaling in decision-making Behavioral game theory and human psychology Ethical and philosophical considerations in strategic choices Case studies and practical applications across various fields Whether you're a student, professional, or curious reader, "Strategic Decisions: The Mathematics of Game Theory" offers not just insights, but a potential transformation in your approach to decision-making. Dive into the world of game theory and let it inspire and motivate you to make strategic choices that can shape your future.

The Complete Idiot's Guide to Game Theory
The Complete Idiot's Guide to Game Theory

Author: Edward C. Rosenthal Ph.D.

Publisher: Penguin

Published: 2011-03-01

Total Pages: 419

ISBN-13: 1101478845

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Gain some insight into the game of life... Game Theory means rigorous strategic thinking. It is based on the idea that everyone acts competitively and in his own best interest. With the help of mathematical models, it is possible to anticipate the actions of others in nearly all life's enterprises. This book includes down-to-earth examples and solutions, as well as charts and illustrations designed to help teach the concept. In The Complete Idiot's Guide® to Game Theory, Dr. Edward C. Rosenthal makes it easy to understand game theory with insights into: • The history of the discipline made popular by John Nash, the mathematician dramatized in the film A Beautiful Mind • The role of social behavior and psychology in this amazing discipline • How important game theory has become in our society and why

Decisions and Elections
Decisions and Elections

Author: Donald Saari

Publisher: Cambridge University Press

Published: 2001-10-22

Total Pages: 258

ISBN-13: 9780521004046

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It is not uncommon to be frustrated by the outcome of an election or a decision in voting, law, economics, engineering, and other fields. Does this 'bad' result reflect poor data or poorly informed voters? Or does the disturbing conclusion reflect the choice of the decision/election procedure? Nobel Laureate Kenneth Arrow's famed theorem has been interpreted to mean 'no decision procedure is without flaws'. Similarly, Nobel Laureate Amartya Sen dashes hope for individual liberties by showing their incompatibility with societal needs. This highly accessible book offers a new, different interpretation and resolution of Arrow's and Sen's theorems. Using simple mathematics, it shows that these negative conclusions arise because, in each case, some of their assumptions negate other crucial assumptions. Once this is understood, not only do the conclusions become expected, but a wide class of other phenomena can also be anticipated.

Mathematical Programming And Game Theory For Decision Making
Mathematical Programming And Game Theory For Decision Making

Author: S K Neogy

Publisher: World Scientific

Published: 2008-04-28

Total Pages: 498

ISBN-13: 9814471240

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This edited book presents recent developments and state-of-the-art review in various areas of mathematical programming and game theory. It is a peer-reviewed research monograph under the ISI Platinum Jubilee Series on Statistical Science and Interdisciplinary Research. This volume provides a panoramic view of theory and the applications of the methods of mathematical programming to problems in statistics, finance, games and electrical networks. It also provides an important as well as timely overview of research trends and focuses on the exciting areas like support vector machines, bilevel programming, interior point method for convex quadratic programming, cooperative games, non-cooperative games and stochastic games. Researchers, professionals and advanced graduates will find the book an essential resource for current work in mathematical programming, game theory and their applications.