| Acknowledgments |
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xv | |
| Introduction |
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xvii | |
| I Static Games of Complete Information |
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1 | (64) |
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Games in Strategic Form and Nash Equilibrium |
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3 | (42) |
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Introduction to Games in Strategic Form and Iterated Strict Dominance |
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4 | (7) |
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4 | (2) |
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6 | (3) |
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Applications of the Elimination of Dominated Strategies |
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9 | (2) |
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11 | (18) |
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Definition of Nash Equilibrium |
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11 | (3) |
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Examples of Pure-Strategy Equilibria |
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14 | (2) |
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Nonexistence of a Pure-Strategy Equilibrium |
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16 | (2) |
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Multiple Nash Equilibria, Focal Points, and Pareto Optimality |
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18 | (5) |
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Nash Equilibrium as the Result of Learning or Evolution |
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23 | (6) |
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Existence and Properties of Nash Equilibria |
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29 | (16) |
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Existence of a Mixed-Strategy Equilibrium |
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29 | (1) |
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The Nash-Equilibrium Correspondence Has a Closed Graph |
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30 | (4) |
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Existence of Nash Equilibrium in Infinite Games with Continuous Payoffs |
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34 | (2) |
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36 | (6) |
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42 | (3) |
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Iterated Strict Dominance, Rationalizability, and Correlated Equilibrium |
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45 | (20) |
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Iterated Strict Dominance and Rationalizability |
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45 | (8) |
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Iterated Strict Dominance: Definition and Properties |
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45 | (2) |
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An Application of Iterated Strict Dominance |
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47 | (1) |
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48 | (2) |
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Rationalizability and Iterated Strict Dominance |
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50 | (3) |
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53 | (1) |
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53 | (6) |
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Rationalizability and Subjective Correlated Equilibria |
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59 | (6) |
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60 | (3) |
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63 | (2) |
| II Dynamic Games of Complete Information |
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65 | (142) |
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67 | (40) |
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67 | (3) |
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Commitment and Perfection in Multi-Stage Games with Observed Actions |
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70 | (7) |
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What Is a Multi-Stage Game? |
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70 | (2) |
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Backward Induction and Subgame Perfection |
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72 | (2) |
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The Value of Commitment and ``Time Consistency'' |
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74 | (3) |
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77 | (6) |
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77 | (5) |
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Multi-Stage Games with Observed Actions |
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82 | (1) |
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Strategies and Equilibria in Extensive-Form Games |
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83 | (9) |
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83 | (2) |
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The Strategic-Form Representation of Extensive-Form Games |
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85 | (2) |
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The Equivalence between Mixed and Behavior Strategies in Games of Perfect Recall |
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87 | (3) |
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Iterated Strict Dominance and Nash Equilibrium |
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90 | (2) |
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Backward Induction and Subgame Perfection |
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92 | (4) |
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Critiques of Backward Induction and Subgame Perfection |
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96 | (11) |
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Critiques of Backward Induction |
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97 | (2) |
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Critiques of Subgame Perfection |
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99 | (1) |
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100 | (5) |
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105 | (2) |
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Applications of Multi-Stage Games with Observed Actions |
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107 | (38) |
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107 | (1) |
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The Principle of Optimality and Subgame Perfection |
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108 | (2) |
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A First Look at Repeated Games |
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110 | (3) |
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The Repeated Prisoner's Dilemma |
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110 | (2) |
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A Finitely Repeated Game with Several Static Equilibria |
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112 | (1) |
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The Rubinstein-Stahl Bargaining Model |
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113 | (4) |
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A Subgame-Perfect Equilibrium |
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113 | (2) |
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Uniqueness of the Infinite-Horizon Equilibrium |
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115 | (1) |
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116 | (1) |
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117 | (11) |
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Definition of Simple Timing Games |
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117 | (3) |
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120 | (6) |
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126 | (2) |
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Iterated Conditional Dominance and the Rubinstein Bargaining Game |
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128 | (2) |
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Open-Loop and Closed-Loop Equilibria |
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130 | (4) |
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130 | (2) |
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132 | (1) |
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Open-Loop and Closed-Loop Equilibria in Games with Many Players |
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133 | (1) |
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Finite-Horizon and Infinite-Horizon Equilibria |
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134 | (11) |
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138 | (3) |
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141 | (4) |
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145 | (62) |
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Repeated Games with Observable Actions |
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146 | (19) |
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146 | (4) |
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The Folk Theorem for Infinitely Repeated Games |
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150 | (10) |
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Characterization of the Equilibrium Set |
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160 | (5) |
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165 | (3) |
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Repeated Games with Varying Opponents |
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168 | (6) |
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Repeated Games with Long-Run and Short-Run Players |
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168 | (3) |
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Games with Overlapping Generations of Players |
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171 | (1) |
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Randomly Matched Opponents |
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172 | (2) |
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Pareto Perfection and Renegotiation-Proofness in Repeated Games |
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174 | (8) |
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174 | (2) |
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Pareto Perfection in Finitely Repeated Games |
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176 | (3) |
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Renegotiation-Proofness in Infinitely Repeated Games |
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179 | (3) |
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Repeated Games with Imperfect Public Information |
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182 | (10) |
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183 | (2) |
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185 | (2) |
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Public Strategies and Public Equilibria |
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187 | (1) |
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Dynamic Programming and Self-Generation |
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188 | (4) |
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The Folk Theorem with Imperfect Public Information |
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192 | (5) |
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Changing the Information Structure with the Time Period |
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197 | (10) |
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200 | (3) |
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203 | (4) |
| III Static Games of Incomplete Information |
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207 | (112) |
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Bayesian Games and Bayesian Equilibrium |
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209 | (34) |
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209 | (2) |
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Example 6.1: Providing a Public Good under Incomplete Information |
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211 | (2) |
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The Notions of Type and Strategy |
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213 | (2) |
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215 | (1) |
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Further Examples of Bayesian Equilibria |
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215 | (11) |
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Deletion of Strictly Dominated Strategies |
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226 | (4) |
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Interim vs. Ex Ante Dominance |
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226 | (2) |
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Examples of Iterated Strict Dominance |
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228 | (2) |
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Using Bayesian Equilibria to Justify Mixed Equilibria |
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230 | (4) |
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230 | (3) |
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233 | (1) |
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The Distributional Approach |
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234 | (9) |
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237 | (4) |
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241 | (2) |
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Bayesian Games and Mechanism Design |
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243 | (76) |
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Examples of Mechanism Design |
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246 | (7) |
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246 | (4) |
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250 | (3) |
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Mechanism Design and the Revelation Principle |
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253 | (5) |
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Mechanism Design with a Single Agent |
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258 | (10) |
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Implementable Decisions and Allocations |
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258 | (4) |
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262 | (6) |
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Mechanisms with Several Agents: Feasible Allocations, Budget Balance, and Efficiency |
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268 | (16) |
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Feasibility under Budget Balance |
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269 | (1) |
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Dominant Strategy vs. Bayesian Mechanisms |
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270 | (1) |
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271 | (4) |
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275 | (4) |
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Efficiency Limit Theorems |
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279 | (2) |
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Strong Inefficiency Limit Theorems |
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281 | (3) |
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Mechanism Design with Several Agents: Optimization |
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284 | (8) |
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284 | (4) |
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Efficient Bargaining Processes |
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288 | (4) |
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Further Topics in Mechanism Design |
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292 | (27) |
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292 | (3) |
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295 | (2) |
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297 | (2) |
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299 | (2) |
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301 | (2) |
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303 | (5) |
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308 | (6) |
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314 | (5) |
| IV Dynamic Games of Incomplete Information |
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319 | (116) |
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Equilibrium Refinements: Perfect Bayesian Equilibrium, Sequential Equilibrium, and Trembling-Hand Perfection |
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321 | (46) |
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321 | (3) |
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Perfect Bayesian Equilibrium in Multi-Stage Games of Incomplete Information |
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324 | (12) |
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324 | (2) |
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Examples of Signaling Games |
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326 | (5) |
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Multi-Stage Games with Observed Actions and Incomplete Information |
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331 | (5) |
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Extensive-Form Refinements |
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336 | (14) |
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336 | (1) |
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337 | (4) |
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Properties of Sequential Equilibrium |
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341 | (4) |
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Sequential Equilibrium Compared with Perfect Bayesian Equilibrium |
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345 | (5) |
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Strategic-Form Refinements |
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350 | (17) |
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Trembling-Hand Perfect Equilibrium |
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351 | (5) |
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356 | (3) |
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359 | (1) |
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360 | (4) |
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364 | (3) |
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367 | (30) |
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367 | (2) |
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Games with a Single Long-Run Player |
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369 | (15) |
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369 | (5) |
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Reputation Effects with a Single Long-Run Player: The General Case |
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374 | (7) |
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Extensive-Form Stage Games |
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381 | (3) |
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Games with Many Long-Run Players |
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384 | (5) |
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General Stage Games and General Reputations |
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384 | (2) |
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Common-Interest Games and Bounded-Recall Reputations |
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386 | (3) |
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A Single ``Big'' Player against Many Simultaneous Long-Lived Opponents |
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389 | (8) |
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391 | (3) |
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394 | (3) |
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Sequential Bargaining under Incomplete Information |
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397 | (38) |
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397 | (3) |
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Intertemporal Price Discrimination: The Single-Sale Model |
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400 | (16) |
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400 | (2) |
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A Two-Period Introduction to Coasian Dynamics |
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402 | (3) |
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An Infinite-Horizon Example of the Coase Conjecture |
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405 | (1) |
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406 | (2) |
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408 | (3) |
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411 | (3) |
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Gap vs. No Gap and Extensions of the Single-Sale Model |
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414 | (2) |
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Intertemporal Price Discrimination: The Rental or Repeated-Sale Model |
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416 | (5) |
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417 | (2) |
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Long-Term Contracts and Renegotiation |
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419 | (2) |
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Price Offers by an Informed Buyer |
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421 | (14) |
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One-Sided Offers and Bilateral Asymmetric Information |
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422 | (2) |
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Alternating Offers and One-Sided Asymmetric Information |
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424 | (3) |
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Mechanism Design and Bargaining |
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427 | (1) |
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428 | (4) |
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432 | (3) |
| V Advanced Topics |
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435 | (138) |
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More Equilibrium Refinements: Stability, Forward Induction, and Iterated Weak Dominance |
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437 | (42) |
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437 | (9) |
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446 | (14) |
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Forward Induction, Iterated Weak Dominance, and ``Burning Money'' |
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460 | (7) |
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Robust Predictions under Payoff Uncertainty |
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467 | (12) |
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473 | (2) |
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475 | (4) |
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Advanced Topics in Strategic-Form Games |
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479 | (22) |
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Generic Properties of Nash Equilibria |
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479 | (5) |
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Number of Nash Equilibria |
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479 | (1) |
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Robustness of Equilibria to Payoff Perturbations |
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480 | (4) |
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Existence of Nash Equilibrium in Games with Continuous Action Spaces and Discontinuous Payoffs |
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484 | (5) |
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Existence of a Pure-Strategy Equilibrium |
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485 | (2) |
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Existence of a Mixed-Strategy Equilibrium |
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487 | (2) |
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489 | (12) |
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497 | (1) |
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498 | (3) |
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Payoff-Relevant Strategies and Markov Equilibrium |
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501 | (40) |
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Markov Equilibria in Specific Classes of Games |
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503 | (10) |
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Stochastic Games: Definition and Existence of MPE |
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503 | (2) |
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Separable Sequential Games |
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505 | (2) |
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507 | (6) |
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Markov Perfect Equilibrium in General Games: Definition and Properties |
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513 | (7) |
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513 | (2) |
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515 | (3) |
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Robustness to Payoff Perturbations |
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518 | (2) |
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520 | (8) |
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520 | (1) |
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521 | (2) |
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Linear-Quadratic Differential Games |
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523 | (2) |
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525 | (2) |
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Zero-Sum Differential Games |
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527 | (1) |
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Capital-Accumulation Games |
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528 | (13) |
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Open-Loop, Closed-Loop, and Markov Strategies |
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529 | (5) |
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Differential-Game Strategies |
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534 | (2) |
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536 | (1) |
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537 | (4) |
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Common Knowledge and Games |
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541 | (32) |
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541 | (1) |
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Knowledge and Common Knowledge |
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542 | (4) |
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Common Knowledge and Equilibrium |
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546 | (8) |
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The Dirty Faces and the Sage |
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547 | (1) |
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548 | (2) |
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550 | (4) |
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Interim Efficiency and Incomplete Contracts |
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554 | (1) |
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Common Knowledge, Almost Common Knowledge, and the Sensitivity of Equilibria to the Information Structure |
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554 | (19) |
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The Lack of Lower Hemi-Continuity |
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556 | (6) |
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Lower Hemi-Continuity and Almost Common Knowledge |
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562 | (8) |
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570 | (1) |
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571 | (2) |
| Index |
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573 | |