Webb J.N. Game Theory: Decisions, Interaction and Evolution

Springer – 2006, 252 pages
ISBN: 1846284236, 9781846284236This 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.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 Dynamics.
Appendices.
Constrained Optimisation.
Dynamical Systems.
Solutions to Exercises.
Further Reading.