Game Theory: Decisions, Interaction and Evolution

Description

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. Front Matter....Pages i-ix Front Matter....Pages 1-1 Simple Decision Models....Pages 3-22 Simple Decision Processes....Pages 23-35 Markov Decision Processes....Pages 37-57 Front Matter....Pages 59-59 Static Games....Pages 61-87 Finite Dynamic Games....Pages 89-105 Games with Continuous Strategy Sets....Pages 107-117 Infinite Dynamic Games....Pages 119-135 Front Matter....Pages 137-137 Population Games....Pages 139-163 Replicator Dynamic....Pages 165-185 Back Matter....Pages 187-241