Date : 2022
Type : Livre / Book
Langue / Language : anglais / English
ISBN : 978-1-316-51633-1
ISBN : 978-1-009-01479-3
EAN : 9781316516331
EAN : 9781009014793
Classification Dewey : 519.3
Collection : London Mathematical Society student texts / managing ed. E.B. Davies / Cambridge : Cambridge University Press , 1986-
Relation : Acourse in stochastic game theory / Eilon Solan / Cambridge : Cambridge University Press
Résumé / Abstract : Stochastic games have an element of chance: the state of the next round is determined probabilistically depending upon players' actions and the current state. Successful players need to balance the need for short-term payoffs while ensuring future opportunities remain high. The various techniques needed to analyze these often highly non-trivial games are a showcase of attractive mathematics, including methods from probability, differential equations, algebra, and combinatorics. This book presents a course on the theory of stochastic games going from the basics through to topics of modern research, focusing on conceptual clarity over complete generality. Each of its chapters introduces a new mathematical tool - including contracting mappings, semi-algebraic sets, infinite orbits, and Ramsey's theorem, among others - before discussing the game-theoretic results they can be used to obtain. The author assumes no more than a basic undergraduate curriculum and illustrates the theory with numerous examples and exercises, with solutions available online.