Games analysis

  • Alexander Shen
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)


In this chapter we consider a basic notion of game theory: a class of games called finite perfect information games. First (section 11.1) we consider some examples that illustrate the notion of a winning strategy. Then in section 11.2 we prove the Zermelo theorem and define the notion of game cost. This leads to an algorithmic question: how can we compute the game cost? In section 11.3 we show an algorithm based on the full traversal of the game tree, and in section 11.4 we study an optimization technique that allows us to compute (exactly) the game cost avoiding some parts of the game tree. Finally, in section 11.5 we apply dynamic programming to gameanalysis.


Winning Strategy Game Tree Terminal Vertex Game Graph Current Vertex 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Laboratoire d’Informatique Fondamentale de Marseille (LIF) CNRSUniversité de la Méditerranée, Université de ProvenceMarseille Cedex 13France
  2. 2.Russian Academy of SciencesInstitute for Information Transmission ProblemsMoscowRussia

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