Home     Giacomo Bonanno
Department of Economics,  University of California, Davis, CA 95616-8578
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Table of contents:
Game Theory
Giacomo Bonanno

Preface.................................................................................................................. 3

Contents ................................................................................................................5  

1. Introduction...................................................................................................... 11

PART I: Games with ordinal payoffs......................................................................15

2. Ordinal games in strategic form..........................................................................17

2.1 Game frames and games

2.2 Strict and weak dominance

2.3 Second-price auction

1.4 The pivotal mechanism

2.5 Iterated deletion procedures

2.6 Nash equilibrium

2.7 Games with infinite strategy sets

2.8 Proofs of theorems

2.9 Exercises [23 exercises]

2.10 Solutions to exercises

3. Perfect information games...............................................................................75

3.1 Trees, frames and games

3.2 Backward induction

3.3 Strategies in perfect-information games

3.4 Relationship between backward induction and other solutions

3.5 Perfect-information games with two players

3.6 Exercises [13 exercises]

3.7 Solutions to exercises

4. General dynamic games.................................................................................117

4.1 Imperfect information

4.2 Strategies

4.3 Subgames

4.4 Subgame-perfect equilibrium

4.5 Games with chance moves

4.6 Exercises [15 exercises]

4.7 Solutions to exercises

 

PART II: Games with cardinal payoffs............................................................. 167

 5. Expected Utility.......................................................................................... 169

            5.1 Money lotteries and attitudes to risk

            5.2 Expected utility: theorems

            5.3 Expected utility: the axioms

            5.4 Exercises [14 exercises]

           5.5 Solutions to exercises

6. Strategic-form games.................................................................................. 193

6.1 Strategic-form games with cardinal payoffs

6.2 Mixed strategies

6.3 Computing the mixed-strategy Nash equilibria

6.4 Strict dominance and rationalizability

6.5 Exercises [15 exercises]

6.6 Solutions to exercises

7. Extensive-form games.................................................................................. 227

7.1 Behavioral strategies in dynamic games

7.2 Subgame-perfect equilibrium revisited

7.3 Problems with subgame-perfect equilibrium

7.4 Exercises [9 exercises]

7.5 Solutions to exercises

 

PART III: Knowledge, common knowledge, belief............................................ 259

8. Common knowledge.................................................................................... 261

            8.1 Individual knowledge

            8.2 Interactive knowledge

            8.3 Common Knowledge

            8.4 Exercises [14 exercises]

            8.5 Solutions to exercises

 

9. Adding beliefs to knowledge........................................................................ 295

            9.1 Sets and probability: brief review

            9.2 Probabilistic beliefs

            9.3 Conditional probability and Bayes’ rule

            9.4 Changing beliefs in response to information

            9.5 Harsanyi consistency of beliefs or like-mindedness

            9.6 Agreeing to disagree

            9.7 Proof of the Agreement Theorem

            9.8 Exercises [28 exercises]

            9.9 Solutions to exercises

 

10. Common knowledge of rationality.................................................................347

            10.1 Models of strategic-form games

            10.2 Common knowledge of rationality in strategic-form games

            10.3 Common knowledge of rationality in extensive-form games

            10.4 Proofs of theorems

            Appendix 9.E: Exercises [7 exercises]

            Appendix 9.S: Solutions to exercises



PART IV: Refinements of subgame-perfect equilibrium..................................... 367

11. Weak Sequential Equilibrium...................................................................... 369

            11.1 Assessments and sequential rationality

            11.2 Bayesian updating at reached information sets

            10.3 A first attempt: Weak sequential equilibrium

           10.4 Exercises [8 exercises]

            10.5 Solutions to exercises.

 

12. Sequential Equilibrium................................................................................ 403

            12.1 Consistent assessments

            12.2 Sequential equilibrium

            12.3 Is ‘consistency’ a good notion?

            12.4 Exercises [6 exercises]

            12.5 Solutions to exercises

 

13. Perfect Bayesian Equilibrium....................................................................... 429

            13.1 Belief revision and AGM consistency

            13.2 Bayesian consistency

            13.3 Perfect Bayesian equilibrium.

            13.4 Adding independence

            13.5 Characterization of SE in temrs of PBE

            13.6 History-based definition of extensive-form game

            13.7  Proofs

            13.8 Exercises [13  exercises]

           13.9 Solutions to exercises

PART V: Incomplete Information...................................................................481

14. Static Games...........................................................................................483

            14.1 Interactive situations with incomplete information

            14.2 One-sided incomplete information

            14.3 Two-sided incomplete information

            14.4 Multi-sided incomplete information

            14.5 Exercises [8 exercises]

            14.6 Solutions to exercises

 

15. Dynamic  Games........................................................................................521

            15.1 One-sided incomplete information

            15.2 Multi-sided incomplete information

            15.3 Exercises [7 exercises]

            15.4 Solutions to exercises

 

16. The type-space approach..................................... 567

            16.1 Types of players

            16.2 Types that know their own payoffs

            16.3 The general case

            16.4 Exercises [4 exercises]

            16.5 Solutions to exercises

 

References....................................................................................................... 585

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