## Stability and Perfection of Nash EquilibriaI have been pleased with the favourable reception of the first edition of this book and I am grateful to have the opportunity to prepare this second edition. In this revised and enlarged edition I corrected some misprints and errors that occurred in the first edition (fortunately I didn't find too many) and I added a large number of notes that give the reader an impression of what kind of results have been obtained since the first edition was printed and that give an indication of the direction the subject is taking. Many of the notes discuss (or refer to papers discussing) applications of the refinements that are considered. Of course, it is the quantity and the quality of the insights and the applications that lend the refinements their validity. Although the guide to the applications is far from complete, the notes certainly allow the reader to form a good judgement of which refinements have really yielded new insights. Hence, as in the first edition, I will refrain from speculating on which refinements of Nash equilibria will survive in the long run. To defend this position let me also cite Binmore [1990] who compares writing about refinements to the Herculean task of defeating the nine-headed Hydra which grew too heads for each that was struck off. It is a pleasure to have the opportunity to thank my secretary, Marjoleine de Wit, who skilfully and, as always, cheerfully typed the manuscript and did the proofreading. |

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### Contents

I | xix |

III | 1 |

IV | 4 |

V | 6 |

VI | 11 |

VII | 15 |

VIII | 18 |

IX | 20 |

XLVIII | 126 |

XLIX | 128 |

LI | 131 |

LII | 134 |

LIII | 139 |

LIV | 143 |

LV | 148 |

LVI | 154 |

X | 24 |

XI | 27 |

XII | 33 |

XIII | 36 |

XIV | 40 |

XV | 43 |

XVI | 44 |

XVIII | 47 |

XIX | 49 |

XX | 52 |

XXI | 55 |

XXII | 60 |

XXIII | 61 |

XXIV | 62 |

XXV | 64 |

XXVI | 66 |

XXVII | 70 |

XXVIII | 72 |

XXIX | 75 |

XXX | 77 |

XXXI | 78 |

XXXII | 79 |

XXXIII | 81 |

XXXIV | 83 |

XXXV | 85 |

XXXVI | 88 |

XXXVII | 91 |

XXXVIII | 94 |

XXXIX | 98 |

XL | 99 |

XLI | 100 |

XLII | 104 |

XLIII | 106 |

XLIV | 111 |

XLV | 115 |

XLVI | 120 |

XLVII | 122 |

LVII | 157 |

LVIII | 162 |

LIX | 164 |

LX | 165 |

LXI | 166 |

LXII | 169 |

LXIII | 173 |

LXIV | 179 |

LXV | 185 |

LXVI | 193 |

LXVII | 196 |

LXVIII | 205 |

LXIX | 209 |

LXX | 212 |

LXXI | 213 |

LXXII | 216 |

LXXIII | 220 |

LXXIV | 224 |

LXXV | 232 |

LXXVI | 238 |

LXXVII | 244 |

LXXVIII | 249 |

LXXIX | 255 |

LXXX | 257 |

LXXXII | 264 |

LXXXIII | 269 |

LXXXIV | 274 |

LXXXV | 280 |

LXXXVI | 294 |

LXXXVII | 298 |

LXXXVIII | 305 |

LXXXIX | 310 |

XC | 316 |

333 | |

XCII | 335 |

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### Common terms and phrases

action agent normal form assume assumption behavior strategy beliefs best reply bimatrix game choose completely mixed condition control costs converges Corollary defined definition denotes direct ESS disturbed game dynamic equilibrium concept equilibrium of F equilibrium outcome equilibrium payoff equilibrium strategy equivalent example exists expected payoff extensive form game finite fixed point follows Furthermore game F game of Fig game theory Harsanyi hence implies incentive to deviate infinitely repeated information set KM-admissible Lemma matrix minmax mistake mixed strategies monopolist Nash equilibrium noncooperative normal form game Note optimal Pareto payoff to player payoff vector perfectness concept perturbed game play probability Proof proper equilibrium pure strategies quasi-strict reduced normal form regular equilibrium renegotiation-proof repeated games resp satisfied Sect Selten sequential equilibrium shown shows signalling games stable set strategy combination strategy of player strictly perfect subgame perfect equilibrium symmetric symmetric equilibrium Theorem undominated unique equilibrium weakly proper zero

### Popular passages

Page v - of which is indeed optimal provided that the other participants conform. Then the question remains as to what will happen if some of the participants do not conform. If that should turn out to be advantageous for them - and, quite particularly, disadvantageous to the conformists - then the above "solution" would seem very questionable.

Page v - The rules of rational behavior must provide definitely for the possibility of irrational conduct on the part of others. In other words: Imagine that we have discovered a set of rules for all

Page xiii - The number of elements of a finite set A is denoted by \A