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Other titles in the Springer Undergraduate Mathematics series:
Game Theory: Decisions, Interaction and Evolution (Springer Undergraduate Mathematics)by James N. Webb
Synopses & Reviews
This book is an informal introduction to game theory intended as a first course for undergraduate students of mathematics. Uniquely, it covers optimal decisions, classical games and evolutionary game theory in one volume. Optimal decisions are treated as a special case of game theory in which the game is played against nature an opponent who is indifferent about the outcome. For evolutionary game theory, a subject which is often presented as a minor adjustment to the classical theory, this book aims to provide a better understanding by emphasising the differences between the two types of game theory, in particular the population context in which evolutionary games are embedded. In contrast to many textbooks at this level, the subject is studied from a mathematical perspective so the emphasis is on presenting the mathematics without getting bogged down in examples which mathematics students, without the relevant background in economics or biology, would struggle to follow, an approach that should also help researchers in biology and economics to understand each other's models. While this book is written primarily for students of mathematics, proofs and other technical discussion are restricted to special cases so this book should be accessible to students and researchers of economics and biology as a second course in the subject or as supplementary reading.
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.
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.
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.
About the Author
James Webb is a former lecturer at Nottingham Trent University, UK
Table of Contents
Part I: Decisions. Simple Decision Models.- Simple Decision Processes.- Markov Decision Processes. Part II: Interaction. Static Games.- Finite Dynamic Games.- Games with Continuous Strategy Sets.- Infinite Dynamic Games. Part III: Evolution. Population Games.- Replicator Dynamics. Part IV: Appendices.- Constrained Optimisation.- Dynamical Systems.- Solutions to Exercises.- Further Reading.- Bibliography.- Index.
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