Game Theory and Partial Differential Equations

Game Theory and Partial Differential Equations
Author: Pablo Blanc
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 234
Release: 2019-07-22
Genre: Mathematics
ISBN: 3110621797

Extending the well-known connection between classical linear potential theory and probability theory (through the interplay between harmonic functions and martingales) to the nonlinear case of tug-of-war games and their related partial differential equations, this unique book collects several results in this direction and puts them in an elementary perspective in a lucid and self-contained fashion.

Emerging Applications of Differential Equations and Game Theory

Emerging Applications of Differential Equations and Game Theory
Author: Alparslan Gök, S?rma Zeynep
Publisher: IGI Global
Total Pages: 284
Release: 2019-11-22
Genre: Mathematics
ISBN: 1799801365

Branches of mathematics and advanced mathematical algorithms can help solve daily problems throughout various fields of applied sciences. Domains like economics, mechanical engineering, and multi-person decision making benefit from the inclusion of mathematics to maximize utility and cooperation across disciplines. There is a need for studies seeking to understand the theories and practice of using differential mathematics to increase efficiency and order in the modern world. Emerging Applications of Differential Equations and Game Theory is a collection of innovative research that examines the recent advancements on interdisciplinary areas of applied mathematics. While highlighting topics such as artificial neuron networks, stochastic optimization, and dynamical systems, this publication is ideally designed for engineers, cryptologists, economists, computer scientists, business managers, mathematicians, mechanics, academicians, researchers, and students.

Game Theory

Game Theory
Author: E. N. Barron
Publisher: John Wiley & Sons
Total Pages: 574
Release: 2013-04-09
Genre: Business & Economics
ISBN: 1118533895

An exciting new edition of the popular introduction to game theory and its applications The thoroughly expanded Second Edition presents a unique, hands-on approach to game theory. While most books on the subject are too abstract or too basic for mathematicians, Game Theory: An Introduction, Second Edition offers a blend of theory and applications, allowing readers to use theory and software to create and analyze real-world decision-making models. With a rigorous, yet accessible, treatment of mathematics, the book focuses on results that can be used to determine optimal game strategies. Game Theory: An Introduction, Second Edition demonstrates how to use modern software, such as MapleTM, Mathematica®, and Gambit, to create, analyze, and implement effective decision-making models. Coverage includes the main aspects of game theory including the fundamentals of two-person zero-sum games, cooperative games, and population games as well as a large number of examples from various fields, such as economics, transportation, warfare, asset distribution, political science, and biology. The Second Edition features: • A new chapter on extensive games, which greatly expands the implementation of available models • New sections on correlated equilibria and exact formulas for three-player cooperative games • Many updated topics including threats in bargaining games and evolutionary stable strategies • Solutions and methods used to solve all odd-numbered problems • A companion website containing the related Maple and Mathematica data sets and code A trusted and proven guide for students of mathematics and economics, Game Theory: An Introduction, Second Edition is also an excellent resource for researchers and practitioners in economics, finance, engineering, operations research, statistics, and computer science.

Differential Games in Economics and Management Science

Differential Games in Economics and Management Science
Author: Engelbert Dockner
Publisher: Cambridge University Press
Total Pages: 398
Release: 2000-11-16
Genre: Business & Economics
ISBN: 9780521637329

A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics.

Partial Differential Equations in Economics and Finance

Partial Differential Equations in Economics and Finance
Author: Suren Basov
Publisher: Nova Publishers
Total Pages: 150
Release: 2007
Genre: Business & Economics
ISBN: 9781600217067

This book reviews the basic theory of partial differential equations of the first and second order and discusses their applications in economics and finance. It starts with well-known applications to consumer and producer theory, and to the theory of option pricing and then introduces new applications that emerge from current research (some of which is the author's own) in bounded rationality, game theory, and multi-dimensional screening.

Stochastic and Differential Games

Stochastic and Differential Games
Author: Martino Bardi
Publisher: Springer Science & Business Media
Total Pages: 388
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461215927

The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L.S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P.P. Varaiya, E. Roxin, R.J. Elliott and N.J. Kalton, N.N. Krasovskii, and A.I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L.D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M.G. Crandall and P.-L.

Game Theory

Game Theory
Author: E. N. Barron
Publisher: John Wiley & Sons
Total Pages: 1
Release: 2013-04-22
Genre: Business & Economics
ISBN: 1118612035

This set includes the following titles: Game Theory: An Introduction, 2nd Edition By: E. N. Barron , PhD ISBN 978-1-118-21693-4 Game Theory: An Introduction, Second Edition offers a blend of theory and applications, allowing readers to use theory and software to create and analyze real-world decision-making models. This book demonstrates how to use modern software, such as Maple™, Mathematica®, and Gambit. Solutions Manual to Accompany Game Theory: An Introduction, 2nd Edition By: E. N. Barron, PhD ISBN: 978-1-118-27428-6 This book provides detailed solutions and explanations to the problems presented in Game Theory: An Introduction, Second Edition. It is a trusted guide and an excellent resource for professors of mathematics and economics and researchers in economics, finance, engineering, operations research, statistics, and computer science.

Differential Games

Differential Games
Author: Rufus Isaacs
Publisher: Courier Corporation
Total Pages: 420
Release: 2012-04-26
Genre: Mathematics
ISBN: 0486135985

Definitive work draws on game theory, calculus of variations, and control theory to solve an array of problems: military, pursuit and evasion, athletic contests, many more. Detailed examples, formal calculations. 1965 edition.

Dynamic Noncooperative Game Theory

Dynamic Noncooperative Game Theory
Author: Tamer Basar
Publisher: SIAM
Total Pages: 526
Release: 1999-01-01
Genre: Mathematics
ISBN: 089871429X

An overview of the analysis of dynamic/differential zero-sum and nonzero-sum games and the role of different information patterns.