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该教材由加州大学伯克利分校的Yuval Peres教授编写，共170多页，本人觉得非常好，比市面上的教材好很多，内容很新。
该博弈论的教材据说以后要正式出版。你下载后会看见，这个教材完全是按照书的样子排版的，我将该书详细的目录贴出来。这本书思路很清晰，不是很厚，适合于仔细阅读。
1 Introduction page 1
2 Combinatorial games 6
2.1 Impartial Games 7
2.1.1 Nim and Bouton's Solution 12
2.1.2 Other Impartial Games 16
2.1.3 Impartial Games and the Sprague-Grundy Theorem 23
2.2 Partisan Games 29
2.2.1 The Game of Hex 32
2.2.2 Topology and Hex: a Path of Arrows* 34
2.2.3 Hex and Y 35
2.2.4 More General Boards* 37
2.2.5 Alternative Representation of Hex 38
2.2.6 Other Partisan Games Played on Graphs 40
3 Two-person zero-sum games 48
3.1 Preliminaries 48
3.2 Von Neumann's Minimax Theorem 52
3.3 The Technique of Domination 56
3.4 The Use of Symmetry 58
3.5 Resistor networks and troll games 60
3.6 Hide-and-seek games 62
3.7 General hide-and-seek games 65
3.8 The bomber and battleship game 67
4 General sum games 74
4.1 Some examples 74
4.2 Nash equilibrium 76
4.3 Correlated Equilibria 80
4.4 General sum games with more than two players 83
ii
Contents iii
4.5 The proof of Nash's theorem 85
4.6 Fixed Point Theorems* 87
4.6.1 Easier Fixed Point Theorems 87
4.6.2 Sperner's lemma 90
4.6.3 Brouwer's Fixed Point Theorem 92
4.7 Evolutionary Game Theory 93
4.7.1 Hawks and Doves 94
4.7.2 Evolutionarily Stable Strategies 96
4.8 Signaling and asymmetric information 101
4.8.1 Examples of signaling (and not) 102
4.8.2 The collapsing used car market 104
4.9 Some further examples 105
4.10 Potential games 106
5 Random-turn and auctioned-turn games 114
5.1 Random-turn games de¯ned 114
5.2 Random-turn selection games 115
5.2.1 Hex 115
5.2.2 Bridg-It 116
5.2.3 Surround 117
5.2.4 Full-board Tic-Tac-Toe 117
5.2.5 Recursive Majority 118
5.2.6 Team captains 118
5.3 Optimal strategy for random-turn selection games 119
5.4 Win-or-lose selection games 121
5.4.1 Length of play for random-turn Recursive Majority 122
5.5 Richman games 123
5.6 Additional notes on Random-turn Hex 126
5.6.1 Odds of winning on large boards and under biased play.126
5.7 Random-turn Bridg-It 127
6 Coalitions and Shapley value 129
6.1 The Shapley value and the glove market 129
6.2 Probabilistic interpretation of Shapley value 132
6.3 Two more examples 135
7 Mechanism design 137
7.1 Auctions 137
7.2 Properties of auction types 138
7.3 Keeping the meteorologist honest 139
7.4 Secret sharing 141
7.4.1 Polynomial Method 143
iv Contents
7.4.2 Private Computation 145
7.5 Cake cutting 146
7.6 Zero Knowledge Proofs 148
7.6.1 Remote Coin Tossing 148
8 Social Choice 150
8.1 Voting Mechanisms and Fairness Criteria 150
8.1.1 Arrow's Fairness Criteria 151
8.2 Examples of Voting Mechanisms 152
8.2.1 Plurality 152
8.2.2 Run-o® Elections 153
8.2.3 Instant Run-o® 154
8.2.4 Borda Count 155
8.2.5 Pairwise Contests 156
8.2.6 Approval Voting 157
8.3 Arrow's impossibility theorem 158
9 Stable matching 161
9.1 Introduction 161
9.2 Algorithms for ¯nding stable matchings 162
9.3 Properties of stable matchings 163
9.4 A Special Preference Order Case 164
Bibliography 165
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