Game Theory

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.

Auteur

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

Texte du rabat

The outstanding feature of this 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. No background knowledge of economics or biology is required as examples have been carefully selected for their accessibility. Detailed solutions to the numerous exercises are provided at the back of the book, making it ideal for self-study. This introduction to game theory is intended as a first course for undergraduate students of mathematics, but it will also interest advanced students or researchers in biology and economics.

Contenu

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.