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Giacomo Bonanno
Department of Economics,  University of California, Davis, CA 95616-8578
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Preface.................................................................................................................. vi

0. Introduction.................................................................................................... 1

PART I: Games with ordinal payoffs........................................................... 5

1. Ordinal games in strategic form

1.1 Game frames and games........................................................................ 6

1.2 Strict and weak dominance.................................................................. 14

1.3 Second-price auction............................................................................ 21

1.4 The pivotal mechanism........................................................................ 24

1.5 Iterated deletion procedures................................................................ 28

1.6 Nash equilibrium.................................................................................. 32

1.7 Games with infinite strategy sets......................................................... 37

Appendix 1.A: Proofs of theorems............................................................. 40

Appendix 1.E: Exercises [23 exercises]...................................................... 43

Appendix 1.S: Solutions to exercises.......................................................... 51

2. Dynamic games with perfect information

2.1 Trees, frames and games...................................................................... 65

2.2 Backward induction............................................................................. 69

2.3 Strategies in perfect-information games............................................... 73

2.4 Relationship between backward induction and
      other solutions..................................................................................... 76

2.5 Perfect-information games with two players........................................ 81

Appendix 2.E: Exercises [13 exercises]...................................................... 84

Appendix 2.S: Solutions to exercises.......................................................... 92

3. General dynamic games

3.1 Imperfect information........................................................................ 107

3.2 Strategies............................................................................................ 114

3.3 Subgames........................................................................................... 116

3.4 Subgame-perfect equilibrium............................................................. 119

3.5 Games with chance moves................................................................. 127

Appendix 3.E: Exercises [14 exercises].................................................... 132

Appendix 3.S: Solutions to exercises........................................................ 139

 

PART II: Games with cardinal payoffs................................................... 157

 4. Expected Utility

            4.1 Money lotteries and attitudes to risk.................................................. 158

            4.2 Expected utility: theorems................................................................. 160

            4.3 Expected utility: the axioms............................................................... 169

            Appendix 4.E: Exercises [14 exercises].................................................... 177

            Appendix 4.S: Solutions to exercises........................................................ 181

5. Mixed strategies in strategic-form games

5.1 Strategic-form games with cardinal payoffs........................................ 186

5.2 Mixed strategies................................................................................. 190

5.3 Computing the mixed-strategy Nash equilibria.................................. 195

5.4 Strict dominance and rationalizability................................................ 201

Appendix 5.E: Exercises [15 exercises].................................................... 205

Appendix 5.S: Solutions to exercises........................................................ 213

6. Dynamic games with cardinal payoffs

6.1 Behavioral strategies in dynamic games............................................. 224

6.2 Subgame-perfect equilibrium revisited............................................... 231

6.3 Problems with subgame-perfect equilibrium...................................... 235

Appendix 6.E: Exercises [9 exercises]...................................................... 237

Appendix 6.S: Solutions to exercises........................................................ 243

 

PART III: Advanced Topics I:
Knowledge, common knowledge, belief................................................. 252

7. Knowledge and common knowledge

            7.1 Individual knowledge......................................................................... 253

            7.2 Interactive knowledge........................................................................ 257

            7.3 Common Knowledge......................................................................... 265

            Appendix 7.E: Exercises [14 exercises].................................................... 272

            Appendix 7.S: Solutions to exercises........................................................ 279

 

8. Adding beliefs to knowledge

            8.1 Probabilistic beliefs............................................................................ 289

            8.2 Conditional probability, belief updating, Bayes’ rule.......................... 292

            8.3 Belief revision.................................................................................... 296

            8.4 Harsanyi consistency of beliefs or like-mindedness........................... 301

            8.5 Agreeing to disagree........................................................................... 306

            Appendix 8.A: Proof of the Agreement Theorem.................................... 315

            Appendix 8.E: Exercises [12 exercises].................................................... 316

            Appendix 8.S: Solutions to exercises........................................................ 323

 

9. Common knowledge of rationality

            9.1 Models of strategic-form games......................................................... 332

            9.2 Common knowledge of rationality in strategic-form games............... 336

            9.3 Common knowledge of rationality in extensive-form games.............. 339

            Appendix 9.A: Proofs............................................................................... 342

            Appendix 9.E: Exercises [7 exercises]...................................................... 344

            Appendix 9.S: Solutions to exercises........................................................ 348



PART IV: Advanced Topics II:
Refinements of subgame-perfect equilibrium......................................... 353

10. A First Attempt: Weak Sequential Equilibrium

            10.1 Assessments and sequential rationality............................................ 354

            10.2 Bayesian updating at reached information sets................................ 361

            10.3 Weak sequential equilibrium............................................................ 363

            Appendix 10.E: Exercises [8 exercises].................................................... 375

            Appendix 10.S: Solutions to exercises...................................................... 380

 

11. Sequential Equilibrium

            11.1 Consistent assessments.................................................................... 389

            11.2 Sequential equilibrium..................................................................... 395

            11.3 Is ‘consistency’ a good notion?........................................................ 397

            Appendix 11.E: Exercises [6 exercises].................................................... 400

            Appendix 11.S: Solutions to exercises...................................................... 406

 

12. Perfect Bayesian Equilibrium

            12.1 Belief revision and AGM consistency.............................................. 418

            12.2 Bayesian consistency........................................................................ 423

            12.3 Perfect Bayesian equilibrium............................................................ 426

            12.4 Adding independence....................................................................... 431

            12.5 Filling the gap between Perfect Bayesian equilibrium
                    and sequential equilibrium............................................................... 434

            Appendix 12.A: History-based definition of extensive-form game........... 443

            Appendix 12.B: Proof of Theorems 12.4................................................. 446

            Appendix 12.E: Exercises [10  exercises]................................................. 448

            Appendix 12.S: Solutions to exercises...................................................... 456

PART V: Advanced Topics III:
Incomplete Information.............................................................................. 470

13. Incomplete Information: Static Games

            13.1 Interactive situations with incomplete information......................... 471

            13.2 One-sided incomplete information.................................................. 473

            13.3 Two-sided incomplete information.................................................. 482

            13.4 Multi-sided incomplete information................................................. 486

            Appendix 13.E: Exercises [8 exercises].................................................... 489

            Appendix 13.S: Solutions to exercises...................................................... 497

 

14. Incomplete Information: Dynamic  Games

            14.1 One-sided incomplete information.................................................. 510

            14.2 Multi-sided incomplete information................................................. 528

            Appendix 14.E: Exercises [7 exercises].................................................... 535

            Appendix 14.S: Solutions to exercises...................................................... 541

 

15. Incomplete Information: the type-space approach

            15.1 Types of players............................................................................... 557

            15.2 Types that know their own payoffs.................................................. 558

            15.3 The general case............................................................................... 563

            Appendix 15.E: Exercises [4 exercises].................................................... 570

            Appendix 15.S: Solutions to exercises...................................................... 566

 

References........................................................................................................ 576

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