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Game Theory Decisions, Interaction and Evolution

ISBN-10: 1846284236

ISBN-13: 9781846284236

Edition: 2007

Authors: James N. Webb

List price: $44.99
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Description:

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 others 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.
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Book details

List price: $44.99
Copyright year: 2007
Publisher: Springer
Publication date: 12/1/2006
Binding: Paperback
Pages: 242
Size: 7.00" wide x 9.25" long x 0.50" tall
Weight: 1.166
Language: English

Decisions
Simple Decision Models
Optimisation
Making Decisions
Modelling Rational Behaviour
Modelling Natural Selection
Optimal Behaviour
Simple Decision Processes
Decision Trees
Strategic Behaviour
Randomising Strategies
Optimal Strategies
Markov Decision Processes
State-dependent Decision Processes
Markov Decision Processes
Stochastic Markov Decision Processes
Optimal Strategies for Finite Processes
Infinite-horizon Markov Decision Processes
Optimal Strategies for Infinite Processes
Policy Improvement
Interaction
Static Games
Interactive Decision Problems
Describing Static Games
Solving Games Using Dominance
Nash Equilibria
Existence of Nash Equilibria
The Problem of Multiple Equilibria
Classification of Games
Games with n-players
Finite Dynamic Games
Game Trees
Nash Equilibria
Information Sets
Behavioural Strategies
Subgame Perfection
Nash Equilibrium Refinements
Games with Continuous Strategy Sets
Infinite Strategy Sets
The Cournot Duopoly Model
The Stackelberg Duopoly Model
War of Attrition
Infinite Dynamic Games
Repeated Games
The Iterated Prisoners' Dilemma
Subgame Perfection
Folk Theorems
Stochastic Games
Evolution
Population Games
Evolutionary Game Theory
Evolutionarily Stable Strategies
Games Against the Field
Pairwise Contest Games
ESSs and Nash Equilibria
Asymmetric Pairwise Contests
Existence of ESSs
Replicator Dynamics
Evolutionary Dynamics
Two-strategy Pairwise Contests
Linearisation and Asymptotic Stability
Games with More Than Two Strategies
Equilibria and Stability
Appendixes
Constrained Optimisation
Dynamical Systems
Solutions
Further Reading
Bibliography
Index