Game Theory: Decisions, Interaction and Evolution

ISBN-13: 9781846284236 / Angielski / Miękka / 2006 / 242 str.

James N. Webb

Opis

This book is an introduction to game theory from a mathematical perspective. It is intended to be a ?rst course for undergraduate students of mathematics, but I also hope that it will contain something of interest to advanced students or researchers in biology and economics who often encounter the basics of game theory informally via relevant applications. In view of the intended audience, the examples used in this book are generally abstract problems so that the reader is not forced to learn a great deal of a subject either biology or e- nomics that may be unfamiliar. Where a context is given, these are usually classical problems of the subject area and are, I hope, easy enough to follow. The prerequisites are generally modest. Apart from a familiarity with (or a willingness to learn) the concepts of a proof and some mathematical no- tion, the main requirement is an elementary understanding of probability. A familiarity with basic calculus would be useful for Chapter 6 and some parts of Chapters 1 and 8. The basic ideas of simple ordinary di?erential equations are required in Chapter 9 and, towards the end of that chapter, some familiarity with matrices would be an advantage although the relevant ideas are brie?y described in an appendix."

Recenzje

"This book is an undergraduate textbook devoted to the study of Game Theory to mathematicians. ... the book is well written and it is one of the best books as a first course in game theory. The book is focused on mathematics students but it can be easily used to students in other fields such as business, economics and biology. ... I strongly recommend this book to the enthusiast of game theory." (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, June, 2016)

"This is supposed to be a mathematical introduction to game theory for undergraduate students. I think both students of economics and mathematics (both with a course of calculus, linear algebra and optimization in Rn) can use this book. The idea of the book is to provide the 'intuition' behind some important theorems of game theory." (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, March, 2014)

"A single-semester elective course in game theory would be an attractive feature of any undergraduate mathematics program. Students would get to use the various mathematical skills they have acquired in a thought-provoking applied context. The book under review is intended as a textbook for such a course. ... Certainly the choice of topics and overall organization is good." (David P. Roberts, MathDL, August, 2007)

Spis treści

Decisions.- Simple Decision Models.- Simple Decision Processes.- Markov Decision Processes.- Interaction.- Static Games.- Finite Dynamic Games.- Games with Continuous Strategy Sets.- Infinite Dynamic Games.- Evolution.- Population Games.- Replicator Dynamic.

O autorze

James Webb is a former lecturer at Nottingham Trent University, UK

Blurb

This introduction to game theory is written from a mathematical perspective. Its primary purpose is to be a first course for undergraduate students of mathematics, but it also contains material which will be of interest to advanced students or researchers in biology and economics.

The outstanding feature of the book is that it provides a unified account of three types of decision problem:

• Situations involving a single decision-maker: in which a sequence of choices is to be made in "a game against nature". This introduces the basic ideas of optimality and decision processes.
• Classical game theory: in which the interactions of two or more decision-makers are considered. This leads to the concept of the Nash equilibrium.
• Evolutionary game theory: in which the changing structure of a population of interacting decision makers is considered. This leads to the ideas of evolutionarily stable strategies and replicator dynamics.

An understanding of basic calculus and probability is assumed but no prior knowledge of game theory is required. Detailed solutions are provided for the numerous exercises.