Game Theory Impartial Combinatorial Games [pdf] - UCLA

GAME THEORY Thomas S. Ferguson Part I. Impartial Combinatorial Games 1. Take-Away Games. 1.1 A Simple Take-Away Game. 1.2 What is a Combinatorial Game? 1.3 P-positions, N-positions. 1.4 Subtraction Games. 1.5 Exercises. 2. The Game of Nim. 2.1 Preliminary... More

GAME THEORY Thomas S. Ferguson Part I. Impartial Combinatorial Games 1. Take-Away Games. 1.1 A Simple Take-Away Game. 1.2 What is a Combinatorial Game? 1.3 P-positions, N-positions. 1.4 Subtraction 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. 2.4 Proof 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. 3.4 The Sprague-Grundy Function on More General Graphs. 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. I – 1 Less