Epistemic Game Theory: Reasoning and Choice

✍ Scribed by Andrés Perea

• Publisher: Cambridge University Press
• Year: 2012
• Tongue: English
• Leaves: 582
• Edition: 1
• Category: Library

✦ Synopsis

In everyday life we must often reach decisions while knowing that the outcome will not only depend on our own choice, but also on the choices of others. These situations are the focus of epistemic game theory. Unlike classical game theory, it explores how people may reason about their opponents before they make their final choice in a game. Packed with examples and practical problems based on stories from everyday life, this is the first textbook to explain the principles of epistemic game theory. Each chapter is dedicated to one particular, natural way of reasoning. The book then shows how each of these ways of reasoning will affect the final choices that can rationally be made and how these choices can be found by iterative procedures. Moreover, it does so in a way that uses elementary mathematics and does not presuppose any previous knowledge of game theory.

✦ Table of Contents

Cover
......Page 1
Epistemic Game Theory......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 8
Figures......Page 12
Tables......Page 14
Acknowledgments......Page 18
1: Introduction......Page 21
Part I: Standard beliefs in static games......Page 31
2.1 Beliefs about the opponent's choice......Page 33
2.2 Utility functions......Page 37
2.3 More than two players......Page 41
2.4 Choosing rationally......Page 45
2.5 Strictly dominated choices......Page 50
2.6 Belief in the opponents' rationality......Page 57
2.7 Graphical method......Page 65
2.8 Algorithm......Page 66
2.9 Proofs......Page 70
2.1 Where to locate a supermarket?......Page 76
2.2 Preparing for a piano exam......Page 77
2.3 Competition between two cinemas......Page 78
2.4 Going to a party......Page 79
2.6 A game of cards......Page 80
2.7 The big race......Page 81
2.10 Zero-sum games......Page 82
Early days of game theory......Page 83
Beliefs and expected utility......Page 84
Randomized choices......Page 85
Examples and problems......Page 86
3.1 Beliefs about the opponents' beliefs......Page 88
3.2 Belief hierarchies......Page 100
3.3 Epistemic model......Page 105
3.4 Common belief in rationality......Page 111
3.5 Graphical method......Page 115
3.6 Existence......Page 118
3.7 Algorithm......Page 122
3.8 Order independence......Page 130
3.9 Proofs......Page 132
3.2 Preparing for a piano exam......Page 138
3.4 Going to a party......Page 139
3.6 Snow White and the seven dwarfs......Page 140
3.7 The mother-in-law......Page 142
3.9 Best-response sets......Page 143
Belief hierarchies and types......Page 144
Alternative ways of describing belief hierarchies......Page 145
Common knowledge and common belief......Page 146
Common belief in rationality......Page 147
Independent beliefs......Page 148
Common prior......Page 149
Best-response sets......Page 150
Large epistemic models......Page 151
The number machine......Page 153
4.1 Simple belief hierarchies......Page 154
4.2 Nash equilibrium......Page 166
4.3 Computational method......Page 170
4.4 Belief that opponents hold correct beliefs......Page 181
4.5 Proofs......Page 187
4.1 Black or white?......Page 191
4.3 To which pub shall I go?......Page 192
4.4 Summer holiday......Page 193
4.5 Playing hide-and-seek......Page 194
4.8 Games with two players and two choices......Page 195
4.9 Zero-sum games......Page 196
Interpretation of Nash equilibrium......Page 197
Sufficient conditions for Nash equilibrium in two-player games......Page 199
Sufficient conditions for Nash equilibrium with more than two players......Page 201
Nash choice versus Nash equilibrium......Page 203
Part II: Lexicographic beliefs in static games
......Page 205
5.1 Cautious reasoning about the opponent......Page 207
5.2 Lexicographic beliefs......Page 210
5.3 Belief hierarchies and types......Page 215
5.4 Cautious types......Page 219
5.5 Primary belief in the opponent's rationality......Page 220
5.6 Common full belief in “primary belief in rationality”......Page 222
5.7 Existence......Page 230
5.8 Weakly dominated choices......Page 233
5.9 Algorithm......Page 235
5.10 Proofs......Page 240
5.1 Painting a room......Page 254
5.3 The closer the better......Page 255
5.4 A walk through the forest......Page 256
5.5 Dinner for two......Page 257
5.7 Stealing an apple......Page 258
5.8 Permissible sets......Page 259
5.10 Full belief in the opponent’s rationality......Page 260
Tension between caution and belief in the opponent’s rationality......Page 261
Alternative ways of modeling cautious reasoning......Page 262
Primary belief in the opponent’s rationality......Page 264
Perfect equilibrium......Page 266
Related concepts......Page 267
6.1 Respecting the opponent's preferences......Page 270
6.2 Common full belief in "respect of preferences''......Page 273
6.3 Existence......Page 278
6.4 Why elimination of choices does not work......Page 281
6.5 Preference restrictions and likelihood orderings......Page 283
6.6 Algorithm......Page 289
6.7 Order independence......Page 296
6.8 Proofs......Page 298
6.3 Planting a tree......Page 312
6.4 A historical trip......Page 313
6.5 Lasergame......Page 314
6.6 A first-price auction......Page 315
6.8 Self-proper sets of preference restrictions......Page 316
6.9 Proper equilibrium......Page 317
Proper rationalizability......Page 318
Proper equilibrium......Page 319
Dividing a pizza......Page 320
7.1 Assuming the opponent's rationality......Page 321
7.2 Common assumption of rationality......Page 325
7.3 Algorithm......Page 334
7.4 Order dependence......Page 340
7.5 Proofs......Page 341
7.1 The closer the better......Page 352
7.2 Stealing an apple......Page 353
7.5 Doing the dishes......Page 354
7.6 Who lets the dog out?......Page 355
7.7 Time to clean the house......Page 356
7.10 Self-admissible pairs of choice sets......Page 357
Assuming the opponent’s rationality......Page 359
Common assumption of rationality......Page 360
Lexicographic rationalizability......Page 362
Self-admissible pairs of choice sets......Page 363
Part III: Conditional beliefs in dynamic games
......Page 365
8.1 Belief revision......Page 367
8.2 Dynamic games......Page 370
8.3 Conditional beliefs......Page 378
8.4 Epistemic model......Page 386
8.5 Belief in the opponents' future rationality......Page 389
8.6 Common belief in future rationality......Page 395
8.7 Existence......Page 399
8.8 Algorithm......Page 403
8.9 Order independence......Page 412
8.10 Backwards order of elimination......Page 417
8.11 Backward induction......Page 430
8.12 Games with unobserved past choices......Page 439
8.13 Bayesian updating......Page 444
8.14 Proofs......Page 448
8.1 Two parties in a row......Page 467
8.2 Selling ice cream......Page 468
8.3 A nightmare with sharks......Page 469
8.5 The street musicians......Page 470
8.6 The three mountains......Page 471
8.7 The Walkin’ Fridge
......Page 472
8.10 Strictly and weakly dominated strategies......Page 473
Strategy......Page 474
Conditional beliefs......Page 475
The problem with “common belief in rationality” in dynamic games......Page 476
Algorithm......Page 478
Subgame perfect equilibrium......Page 479
Sequential equilibrium......Page 480
Sequential rationalizability......Page 482
Backward induction......Page 483
Backward induction paradoxes......Page 484
Common initial belief in rationality......Page 485
One-deviation property......Page 486
Examples and exercises......Page 487
9.1 Strong belief in the opponents' rationality......Page 488
9.2 Common strong belief in rationality......Page 493
9.3 Algorithm......Page 503
9.4 Comparison with backward dominance procedure......Page 513
9.5 Order dependence......Page 521
9.6 Rationality orderings......Page 523
9.7 Bayesian updating......Page 534
9.8 Proofs......Page 535
9.2 Selling ice cream......Page 557
9.3 Watching TV with Barbara......Page 558
9.4 Never let a lady wait......Page 559
9.5 Dinner for three......Page 560
9.6 Read my mind......Page 561
9.7 Time to say goodbye......Page 562
9.9 Initial belief in the opponents’ rationality......Page 563
9.10 A property of the iterated conditional dominance procedure......Page 564
Common strong belief in rationality......Page 565
Order (in) dependence......Page 566
Common strong belief in rationality and backward induction......Page 567
Bayesian updating......Page 568
Forward induction......Page 569
Explicable equilibrium......Page 570
Burning-money games......Page 571
Bibliography......Page 572
Index......Page 579