Giacomo
BonannoDepartment of Economics, University of California, Davis, CA 95616-8578
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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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