Preface |
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xi | |
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PART I Rational Decision Making |
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Chapter 1 The Single-Person Decision Problem |
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3 | (11) |
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1.1 Actions, Outcomes, and Preferences |
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4 | (5) |
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1.1.1 Preference Relations |
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5 | (2) |
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7 | (2) |
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1.2 The Rational Choice Paradigm |
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9 | (2) |
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11 | (1) |
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11 | (3) |
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Chapter 2 Introducing Uncertainty and Time |
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14 | (29) |
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2.1 Risk, Nature, and Random Outcomes |
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14 | (4) |
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2.1.1 Finite Outcomes and Simple Lotteries |
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15 | (1) |
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2.1.2 Simple versus Compound Lotteries |
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16 | (1) |
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2.1.5 Lotteries over Continuous Outcomes |
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17 | (1) |
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2.2 Evaluating Random Outcomes |
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18 | (6) |
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2.2.1 Expected Payoff: The Finite Case |
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19 | (1) |
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2.2.2 Expected Payoff: The Continuous Case |
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20 | (1) |
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2.2.3 Caveat: It's Not Just the Order Anymore |
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21 | (1) |
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22 | (1) |
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2.2.5 The St. Petersburg Paradox |
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23 | (1) |
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2.3 Rational Decision Making with Uncertainty |
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24 | (2) |
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2.3.1 Rationality Revisited |
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24 | (1) |
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2.3.2 Maximizing Expected Payoffs |
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24 | (2) |
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26 | (3) |
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26 | (2) |
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2.4.2 Discounting Future Payoffs |
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28 | (1) |
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29 | (3) |
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2.5.1 The Value of Information |
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29 | (2) |
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2.5.2 Discounted Future Consumption |
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31 | (1) |
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2.6 Theory versus Practice |
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32 | (1) |
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33 | (1) |
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33 | (10) |
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PART II Static Games of Complete Information |
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43 | (16) |
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3.1 Normal-Form Games with Pure Strategies |
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46 | (4) |
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3.1.1 Example: The Prisoner's Dilemma |
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48 | (1) |
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3.1.2 Example: Cournot Duopoly |
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49 | (1) |
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3.1.3 Example: Voting on a New Agenda |
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49 | (1) |
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3.2 Matrix Representation: Two-Player Finite Game |
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50 | (2) |
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3.2.1 Example: The Prisoner's Dilemma |
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51 | (1) |
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3.2.2 Example: Rock-Paper-Scissors |
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52 | (1) |
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52 | (5) |
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3.3.1 Assumptions and Setup |
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54 | (1) |
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3.3.2 Evaluating Solution Concepts |
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55 | (1) |
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3.3.3 Evaluating Outcomes |
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56 | (1) |
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57 | (1) |
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58 | (1) |
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Chapter 4 Rationality and Common Knowledge |
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59 | (20) |
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4.1 Dominance in Pure Strategies |
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59 | (4) |
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4.1.1 Dominated Strategies |
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59 | (2) |
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4.1.2 Dominant Strategy Equilibrium |
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61 | (1) |
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4.1.3 Evaluating Dominant Strategy Equilibrium |
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62 | (1) |
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4.2 Iterated Elimination of Strietly Dominated Pure Strategies |
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63 | (6) |
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4.2.1 Iterated Elimination and Common Knowledge of Rationality |
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63 | (2) |
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4.2.2 Example: Cournot Duopoly |
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65 | (2) |
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67 | (2) |
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4.3 Beliefs, Best Response, and Rationalizability |
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69 | (7) |
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69 | (2) |
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4.3.2 Beliefs and Best-Response Correspondences |
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71 | (2) |
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73 | (1) |
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4.3.4 The Cournot Duopoly Revisited |
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73 | (1) |
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4.3.5 The "p-Beauty Contest" |
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74 | (2) |
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4.3.6 Evaluating Rationalizability |
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76 | (1) |
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76 | (1) |
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76 | (3) |
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Chapter 5 Pinning Down Beliefs: Nash Equilibrium |
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79 | (22) |
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5.1 Nash Equilibrium in Pure Strategies |
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80 | (3) |
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5.1.1 Pure-Strategy Nash Equilibrium in a Matrix |
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81 | (2) |
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5.1.2 Evaluating the Nash Equilibria Solution |
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83 | (1) |
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5.2 Nash Equilibrium: Some Classic Applications |
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83 | (12) |
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5.2.1 Two Kinds of Societies |
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83 | (1) |
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5.2.2 The Tragedy of the Commons |
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84 | (3) |
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87 | (1) |
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88 | (5) |
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5.2.5 Political Ideology and Electoral Competition |
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93 | (2) |
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95 | (1) |
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95 | (6) |
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Chapter 6 Mixed Strategies |
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101 | (28) |
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6.1 Strategies, Beliefs, and Expected Payoffs |
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102 | (5) |
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6.1.1 Finite Strategy Sets |
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102 | (2) |
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6.1.2 Continuous Strategy Sets |
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104 | (1) |
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6.1.3 Beliefs and Mixed Strategies |
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105 | (1) |
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105 | (2) |
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6.2 Mixed-Strategy Nash Equilibrium |
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107 | (7) |
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6.2.1 Example: Matching Pennies |
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108 | (3) |
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6.2.2 Example: Rock-Paper-Scissors |
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111 | (2) |
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6.2.3 Multiple Equilibria: Pure and Mixed |
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113 | (1) |
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6.3 IESDS and Rationalizability Revisited |
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114 | (3) |
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6.4 Nash's Existence Theorem |
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117 | (6) |
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123 | (1) |
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123 | (6) |
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PART III Dynamic Games of Complete Information |
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129 | (22) |
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7.1 The Extensive-Form Game |
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130 | (7) |
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132 | (4) |
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7.1.2 Imperfect versus Perfect Information |
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136 | (1) |
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7.2 Strategies and Nash Equilibrium |
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137 | (8) |
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137 | (2) |
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7.2.2 Mixed versus Behavioral Strategies |
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139 | (4) |
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7.2.3 Normal-Form Representation of Extensive-Form Games |
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143 | (2) |
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7.3 Nash Equilibrium and Paths of Play |
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145 | (2) |
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147 | (1) |
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147 | (4) |
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Chapter 8 Credibility and Sequential Rationality |
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151 | (24) |
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8.1 Sequential Rationality and Backward Induction |
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152 | (1) |
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8.2 Subgame-Perfect Nash Equilibrium: Concept |
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153 | (6) |
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8.3 Subgame-Perfect Nash Equilibrium: Examples |
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159 | (10) |
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159 | (1) |
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8.3.2 Stackelberg Competition |
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160 | (3) |
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8.3.3 Mutually Assured Destruction |
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163 | (3) |
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8.3.4 Time-Inconsistent Preferences |
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166 | (3) |
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169 | (1) |
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170 | (5) |
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Chapter 9 Multistage Games |
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175 | (15) |
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176 | (1) |
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177 | (1) |
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9.3 Strategies and Conditional Play |
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178 | (2) |
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9.4 Subgame-Perfect Equilibria |
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180 | (4) |
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9.5 The One-Stage Deviation Principle |
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184 | (2) |
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186 | (1) |
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186 | (4) |
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Chapter 10 Repeated Games |
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190 | (30) |
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10.1 Finitely Repeated Games |
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190 | (2) |
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10.2 Infinitely Repeated Games |
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192 | (4) |
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193 | (2) |
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195 | (1) |
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10.3 Subgame-Perfect Equilibria |
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196 | (5) |
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10.4 Application: Tacit Collusion |
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201 | (3) |
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10.5 Sequential Interaction and Reputation |
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204 | (5) |
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10.5.1 Cooperation as Reputation |
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204 | (1) |
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10.5.2 Third-Party Institutions as Reputation Mechanisms |
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205 | (2) |
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10.5.3 Reputation Transfers without Third Parties |
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207 | (2) |
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10.6 The Folk Theorem: Almost Anything Goes |
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209 | (5) |
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214 | (1) |
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215 | (5) |
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Chapter 11 Strategic Bargaining |
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220 | (21) |
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11.1 One Round of Bargaining: The Ultimatum Game |
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222 | (2) |
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11.2 Finitely Many Rounds of Bargaining |
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224 | (4) |
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11.3 The Infinite-Horizon Game |
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228 | (1) |
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11.4 Application: Legislative Bargaining |
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229 | (6) |
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11.4.1 Closed-Rule Bargaining |
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230 | (2) |
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11.4.2 Open-Rule Bargaining |
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232 | (3) |
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235 | (1) |
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236 | (5) |
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PART IV Static Games of Incomplete Information |
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Chapter 12 Bayesian Games |
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241 | (29) |
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12.1 Strategic Representation of Bayesian Games |
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246 | (6) |
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12.1.1 Players, Actions, Information, and Preferences |
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246 | (1) |
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12.1.2 Deriving Posteriors from a Common Prior: A Player's Beliefs |
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247 | (2) |
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12.1.3 Strategies and Bayesian Nash Equilibrium |
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249 | (3) |
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252 | (6) |
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12.2.1 Teenagers and the Game of Chicken |
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252 | (3) |
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255 | (3) |
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12.3 Inefficient Trade and Adverse Selection |
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258 | (3) |
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261 | (3) |
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12.5 Mixed Strategies Revisited: Harsanyi's Interpretation |
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264 | (2) |
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266 | (1) |
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266 | (4) |
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Chapter 13 Auctions and Competitive Bidding |
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270 | (18) |
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13.1 Independent Private Values |
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272 | (10) |
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13.1.1 Second-Price Sealed-Bid Auctions |
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272 | (3) |
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275 | (1) |
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13.1.3 First-Price Sealed-Bid and Dutch Auctions |
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276 | (3) |
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13.1.4 Revenue Equivalence |
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279 | (3) |
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13.2 Common Values and the Winner's Curse |
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282 | (3) |
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285 | (1) |
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285 | (3) |
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Chapter 14 Mechanism Design |
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288 | (15) |
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14.1 Setup: Mechanisms as Bayesian Games |
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288 | (4) |
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288 | (1) |
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14.1.2 The Mechanism Designer |
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289 | (1) |
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14.1.3 The Mechanism Game |
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290 | (2) |
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14.2 The Revelation Principle |
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292 | (3) |
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14.3 Dominant Strategies and Vickrey-Clarke-Groves Mechanisms |
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295 | (4) |
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14.3.1 Dominant Strategy Implementation |
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295 | (1) |
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14.3.2 Vickrey-Clarke-Groves Mechanisms |
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295 | (4) |
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299 | (1) |
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299 | (4) |
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PART V Dynamic Games of Incomplete Information |
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Chapter 15 Sequential Rationality with Incomplete Information |
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303 | (15) |
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15.1 The Problem with Subgame Perfection |
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303 | (4) |
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15.2 Perfect Bayesian Equilibrium |
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307 | (5) |
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15.3 Sequential Equilibrium |
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312 | (2) |
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314 | (1) |
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314 | (4) |
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Chapter 16 Signaling Games |
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318 | (21) |
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16.1 Education Signaling: The MBA Game |
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319 | (4) |
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16.2 Limit Pricing and Entry Deterrence |
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323 | (9) |
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16.2.1 Separating Equilibria |
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324 | (6) |
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16.2.2 Pooling Equilibria |
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330 | (2) |
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16.3 Refinements of Perfect Bayesian Equilibrium in Signaling Games |
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332 | (3) |
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335 | (1) |
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335 | (4) |
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Chapter 17 Building a Reputation |
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339 | (18) |
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17.1 Cooperation in a Finitely Repeated Prisoner's Dilemma |
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339 | (3) |
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17.2 Driving a Tough Bargain |
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342 | (7) |
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17.3 A Reputation for Being "Nice" |
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349 | (5) |
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354 | (1) |
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354 | (3) |
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Chapter 18 Information Transmission and Cheap Talk |
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357 | (12) |
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18.1 Information Transmission: A Finite Example |
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358 | (3) |
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18.2 Information Transmission: The Continuous Case |
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361 | (4) |
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18.3 Application: Information and Legislative Organization |
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365 | (2) |
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367 | (1) |
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367 | (2) |
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Chapter 19 Mathematical Appendix |
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369 | (16) |
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369 | (2) |
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369 | (1) |
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19.1.2 Basic Set Operations |
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370 | (1) |
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371 | (2) |
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371 | (1) |
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372 | (1) |
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19.3 Calculus and Optimization |
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373 | (5) |
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373 | (1) |
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19.3.2 Differentiation and Optimization |
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374 | (3) |
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377 | (1) |
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19.4 Probability and Random Variables |
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378 | (7) |
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378 | (1) |
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19.4.2 Cumulative Distribution and Density Functions |
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379 | (1) |
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19.4.3 Independence, Conditional Probability, and Bayes' Rule |
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380 | (2) |
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382 | (3) |
References |
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385 | (4) |
Index |
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