Game Theory Basics

2021 ◽  
Author(s):  
Bernhard von Stengel
Keyword(s):  
Game Theory ◽  
Imperfect Information ◽  
Direct Proof ◽  
Minimax Theorem ◽  
Introductory Courses ◽  
Game Trees ◽  
Self Study ◽  
Or Economics ◽  
Zero Sum ◽  
Non Cooperative Games

Game theory is the science of interaction. This textbook, derived from courses taught by the author and developed over several years, is a comprehensive, straightforward introduction to the mathematics of non-cooperative games. It teaches what every game theorist should know: the important ideas and results on strategies, game trees, utility theory, imperfect information, and Nash equilibrium. The proofs of these results, in particular existence of an equilibrium via fixed points, and an elegant direct proof of the minimax theorem for zero-sum games, are presented in a self-contained, accessible way. This is complemented by chapters on combinatorial games like Go; and, it has introductions to algorithmic game theory, traffic games, and the geometry of two-player games. This detailed and lively text requires minimal mathematical background and includes many examples, exercises, and pictures. It is suitable for self-study or introductory courses in mathematics, computer science, or economics departments.

MONTE CARLO METHODS IN FUZZY GAME THEORY

2007 ◽  
Vol 03 (02) ◽  
pp. 259-269 ◽  
Author(s):  
AREEG ABDALLA ◽  
JAMES BUCKLEY
Keyword(s):  
Game Theory ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Mixed Strategy ◽  
Minimax Theorem ◽  
Approximate Solutions ◽  
Mixed Strategies ◽  
Fuzzy Game ◽  
Zero Sum

In this paper, we consider a two-person zero-sum game with fuzzy payoffs and fuzzy mixed strategies for both players. We define the fuzzy value of the game for both players [Formula: see text] and also define an optimal fuzzy mixed strategy for both players. We then employ our fuzzy Monte Carlo method to produce approximate solutions, to an example fuzzy game, for the fuzzy values [Formula: see text] for Player I and [Formula: see text] for Player II; and also approximate solutions for the optimal fuzzy mixed strategies for both players. We then look at [Formula: see text] and [Formula: see text] to see if there is a Minimax theorem [Formula: see text] for this fuzzy game.

Legal Disputes Resolved via Game Theoretic Methods

2015 ◽  
Vol 17 (02) ◽  
pp. 1540015 ◽  
Author(s):  
T. E. S. Raghavan
Keyword(s):  
Game Theory ◽  
Solution Concept ◽  
Hourly Wage ◽  
Old Babylonian ◽  
Solution Methods ◽  
Game Theoretic ◽  
Person Game ◽  
Zero Sum ◽  
Mathematical Foundations ◽  
Non Cooperative Games

Mathematical foundations of conflict resolutions are deeply rooted in the theory of cooperative and non-cooperative games. While many elementary models of conflicts are formalized, one often raises the question whether game theory and its mathematically developed tools are applicable to actual legal disputes in practice. We choose an example from union management conflict on hourly wage dispute and how zero sum two person game theory can be used by a judge to bring about the need for realistic compromises between the two parties. We choose another example from the 2000-year old Babylonian Talmud to describe how a certain debt problem was resolved. While they may be unaware of cooperative game theory, their solution methods are fully consistent with the solution concept called the nucleolus of a TU game.

John von Neumann's Contribution to Modern Game Theory

2004 ◽  
Vol 54 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Ferenc Forgó
Keyword(s):  
Game Theory ◽  
Cooperative Games ◽  
Minimax Theorem ◽  
Stable Set ◽  
Zero Sum Games ◽  
Side Payments ◽  
Basic Concepts ◽  
Definition Of ◽  
Zero Sum ◽  
Abstract Games

The paper gives a brief account of von Neumann's contribution to the foundation of game theory: definition of abstract games, the minimax theorem for two-person zero-sum games and the stable set solution for cooperative games with side payments. The presentation is self-contained, uses very little mathematical formalism and caters to the nonspecialist. Basic concepts and their implications are in focus. It is also indicated how von Neumann's groundbreaking work initiated further research, and a few unsolved problems are also mentioned.

Pelé Meets John Von Neumann in the Penalty Area

2014 ◽  
Author(s):  
Ignacio Palacios-Huerta
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
General Theory ◽  
Minimax Theorem ◽  
Common Interest ◽  
John Von Neumann ◽  
Von Neumann ◽  
Complete Test ◽  
Zero Sum ◽  
Special Case

The movie A Beautiful Mind (2001) portrays the life and work of John F. Nash Jr., who received the Nobel Prize in Economics in 1994. A class of his theories deals with how people should behave in strategic situations that involve what are known as “mixed strategies,” that is, choosing among various possible strategies when no single one is always the best when you face a rational opponent. This chapter uses data from a specific play in soccer (a penalty kick) with professional players to provide the first complete test of a fundamental theorem in game theory: the minimax theorem. The minimax theorem can be regarded as a special case of the more general theory of Nash. It applies only to two-person, zero-sum or constant-sum games, whereas the Nash equilibrium concept can be used with any number of players and any mixture of conflict and common interest in the game.

Noncooperative Game Theory

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Game Theory ◽  
Computer Science ◽  
Dynamic Games ◽  
Design Methodology ◽  
Noncooperative Game ◽  
Noncooperative Game Theory ◽  
Original Design ◽  
Theoretical Perspectives ◽  
Engineering Designs ◽  
Zero Sum

This book is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. The book shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each problem's essence: Who are the players? What are their goals? Will the solution to “the game” solve the original design problem? Using the fundamentals of game theory, the book explores these issues and more. The use of game theory in technology design is a recent development arising from the intrinsic limitations of classical optimization-based designs. In optimization, one attempts to find values for parameters that minimize suitably defined criteria—such as monetary cost, energy consumption, or heat generated. However, in most engineering applications, there is always some uncertainty as to how the selected parameters will affect the final objective. Through a sequential and easy-to-understand discussion, the book examines how to make sure that the selection leads to acceptable performance, even in the presence of uncertainty—the unforgiving variable that can wreck engineering designs. The book looks at such standard topics as zero-sum, non-zero-sum, and dynamic games and includes a MATLAB guide to coding. This book offers students a fresh way of approaching engineering and computer science applications.

scholarly journals A computational model of outguessing in two-player non-cooperative games

2014 ◽  
Vol 6 (1) ◽  
pp. 71-88
Author(s):  
Tamás László Balogh ◽  
János Kormos
Keyword(s):  
Numerical Simulation ◽  
Computational Model ◽  
Cooperative Games ◽  
Behavioral Game Theory ◽  
Equilibrium Concept ◽  
Zero Sum Games ◽  
Simulation Based ◽  
Behavioral Game ◽  
Zero Sum ◽  
Non Cooperative Games

Abstract Several behavioral game theory models aim at explaining why “smarter“ people win more frequently in simultaneous zero-sum games, a phanomenon, which is not explained by the Nash equilibrium concept. We use a computational model and a numerical simulation based on Markov chains to describe player behavior and predict payoffs.

Zero-sum game theory model for segmenting skin regions

2020 ◽  
Vol 99 ◽  
pp. 103925
Author(s):  
Djamila Dahmani ◽  
Mehdi Cheref ◽  
Slimane Larabi
Keyword(s):  
Game Theory ◽  
Theory Model ◽  
Zero Sum

EXPERIENCE OF THE GAME THEORY APPLICATION IN CONSTRUCTION MANAGEMENT / LOŠIMŲ TEORIJOS TAIKYMO PATIRTIS STATYBOS VADYBOJE

2008 ◽  
Vol 14 (4) ◽  
pp. 531-545 ◽  
Author(s):  
Friedel Peldschus
Keyword(s):  
Game Theory ◽  
Solution Strategies ◽  
Conflict Situations ◽  
Engineering Problems ◽  
The Game Theory ◽  
Potential Applications ◽  
Fuzzy Games ◽  
Theory Application ◽  
Construction Operation ◽  
Zero Sum

The game theory allows mathematical solutions of conflict situations. Besides the fairly established application to economical problems, approaches to problems in construction operation have been worked out. An overview of applications is given. Solution strategies for such engineering problems are collected. Furthermore, concrete application examples are presented and an overview of further potential applications is given. Solutions of two‐person zero‐sum games are discussed as well as approaches to fuzzy games. Santrauka Lošimų teorija teikia matematinių sprendimų konfliktinėse situacijose. Straipsnyje pateikta daug ekonominių problemų sprendimo pavyzdžių, sukurtų statybos valdymo problemų sprendimo metodikų. Atlikta šių tyrimų apžvalga, surinktos minėtų inžinerinių problemų sprendimo strategijos. Pateikiami konkretūs teorijos taikymo pavyzdžiai dabarties sąlygomis ir ateityje. Aptariami „dviejų asmenų nulinės sumos“ lošimų sprendiniai, taip pat neapibrėžtų aibių teorijos taikymo lošimuose atveju.

Game theory and its economic applications

2018 ◽  
Author(s):  
Анатолий Сигал ◽  
Anatoliy Sigal
Keyword(s):  
Game Theory ◽  
Matrix Games ◽  
Managerial Decisions ◽  
Combined Application ◽  
Finite Games ◽  
Basic Concepts ◽  
Zero Sum ◽  
Risk Managers ◽  
Large Groups ◽  
Antagonistic Games

The manual describes the main sections of game theory, the basic concepts of the theory of economic risks and the conceptual framework for modeling the process of making managerial decisions in the economy based on the combined application of statistical and antagonistic games. Antagonistic games (AG) are the finite games of two persons with zero sum, i.e. matrix games, with classical antagonistic games called AG, given by completely known matrices, and neoclassical antagonistic games – AG, given by partially known matrices. The manual is intended primarily for masters who study in the direction of training "business information". However, it will be useful for students and postgraduates studying in large groups of areas of training "Economics and Management", "Mathematics and Mechanics", "Management in Technical Systems", as well as scientific and pedagogical workers specializing in the field of the theory of games, risk managers , managers and economists-practitioners.

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