The outstanding feature of the book is that it provides a unified account of three types of decision problem. It covers the basic ideas of decision theory, classical game theory, and evolutionary game theory in one volume.

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 someparts 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.

Provides three books in one: it covers the basic ideas of decision theory, classical game theory; and evolutionary game theory in one volume No background knowledge of economics or biology is required: examples have been carefully selected to be accessible to readers unfamiliar with these subjects Detailed solutions to the numerous exercises are provided at the back of the book, making it ideal for self-study

Autorentext

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

Klappentext
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.

Inhalt
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.