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.
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