加州大学洛杉矶分析初级GAME THEORY课件

Thomas S. Ferguson教授
1. Take-Away Games.
1.1 A Simple Take-Away Game.
1.2 What is a Combinatorial Game?
1.3 P-positions, N-positions.
1.4Subt raction Games.
1.5 Exercises.
2. The Game of Nim.
2.1 Preliminary Analysis.
2.2 Nim-Sum.
2.3 Nim With a Larger Number of Piles.
2.4Pr oof of Bouton’s Theorem.
2.5 Mis`ere Nim.
2.6 Exercises.
3. Graph Games.
3.1 Games Played on Directed Graphs.
3.2 The Sprague-Grundy Function.
3.3 Examples.
3.4T he Use of the Sprague-Grundy Function.
3.5 Exercises.
4. Sums of Combinatorial Games.
4.1 The Sum of n Graph Games.
4.2 The Sprague Grundy Theorem.
4.3 Applications.
4.4 Take-and-Break Games.
4.5 Exercises.
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5. Green Hackenbush.
5.1 Bamboo Stalks.
5.2 Green Hackenbush on Trees.
5.3 Green Hackenbush on General Rooted Graphs.
5.4Exer cises.