Game theory is one of the success stories of modern economics. Originally concerned with gambling, it has since become part of the standard toolkit of social scientists, biologists, psychologists, political scientists -- even historians and philosophers! This course is an introduction to the methods and applications of game theory. It is designed to stimulate careful thinking about the use (and potential abuse) of mathematics as an instrument for the formal study of strategic behaviour. It also provides empirical evidence on these interactions.

## I. Pure game theory

### 1. Fundamentals of game theory

- Solution concepts (Lecture 1, Lecture 2)
- Bayesian games (Lecture 4)
- Global games (Lecture 5)
- Voting games (Lecture 6)
- Behavioral game theory (Lecture 3)

#### Assignments

*Week 2*: Problem set 1, problems 1, 2 and 3; problem set 2, problem 1.

*Week 3*: Problem set 2, problems 2 and 3; problem set 3, problem 2.

#### Suggested readings

- MO chapters 2 (Nash equilibrium), 4 (mixed-strategy equilibrium), 9 (Bayesian games) and 12 (rationalizability).
- Chiappori, P., S. Levitt, and T. Groseclose, 'Testing Mixed-Strategy Equilibria when Players are Heterogeneous: The Case of Penalty Kicks in Soccer',
*American Economic Review*, 92 (2002), 1138--1151. - Diamond, D. 'Banks and Liquidity Creation: A Simple Exposition of the Diamond-Dybvig Model',
*Economics Quarterly*, 93 (2007), 189–200. - van den Assem, M., D. van Dolder and R. Thaler. 2012. 'Split or Steal? Cooperative Behavior when the Stakes are Large',
*Management Science*, 58(1): 2–20.

### 2. Refinements for dynamic and repeated games

- Dynamic games (Lecture 7)
- Refinements (Lecture 8)
- Repeated games (Lecture 17 and Lecture 18)

#### Assignments

*Week 4*: Problem set 4, problems 1 to 3.

*Week 5*: Problem set 8, problems 1 to 3.

#### Suggested readings

- MO chapters 5, 6, 7 (extensive games with perfect information), 10 up to 10.4 included (extensive games with imperfect information), 14 and 15 (repeated games).
- Abreu, D., D. Pierce and E. Stacchetti. 1986. 'Optimal Cartel Equilibria with Imperfect Monitoring',
*Journal of Economic Theory*, 39: 251–269. [The introduction and conclusion to this article are enough–all the rest is*very*technical and way beyond the scope of this course.] - Aumann, R. 1995. 'Backward Induction and Common Knowledge of Rationality',
*Games and Economic Behavior*, 8(1): 6–19. - Eso, P. and J. Schummer. 2009. 'Credible Deviations from Signaling Equilibria',
*International Journal of Game Theory*, 38(3): 411–430. - Farrell, J. and E. Maskin. 1989. 'Renegotiation in Repeated Games',
*Games and Economic Behavior*, 1(4): 327–360.

## II. Applied game theory: Who gets what–and why?

### 1. Auctions and mechanism design

- Auction theory (my lecture notes)
- Mechanism design (Lecture 16)

#### Assignments

*Week 6*: Essay (see Additional assignments), which must be between 900 and 1100 words in length (excluding references). Your answer should demonstrate in-depth understanding of the question in relation to concepts from the course, but will also be assessed on the quality of written expression, the argumentative structure, and engagement with the literature.

*Week 7*: Problems A, B and C (see Additional assignments); problem set 7, problem 2.

#### Suggested readings

- Krishna, V. 2002.
*Auction Theory*, Academic Press. [Chapter 5 (mechanism design)]. - Klemperer, P. 2004.
*Auctions: Theory and Practice*, Princeton University Press. [Part A and the associated appendix.] - Athey, S., J. Levin and E. Seira. 2011. 'Comparing open and sealed bid auctions: Evidence from timber
auctions',
*Quarterly Journal of Economics*, 126(1): 207–257. - Myerson, R. 1981. 'Optimal Auction Design',
*Mathematics of Operations Research*, 6(1): 58–73. [The proofs of Lemma 2 (which became Myerson’s Lemma) and its corollary (the Revenue Equivalence Theorem) are particularly instructive.] - Vickrey, W. 1961. 'Counterspeculation, Auctions, and Competitive Sealed Tenders',
*Journal of Finance*, 16(1): 8–37. [The most interesting sections for this purpose are II and especially III, where Vickrey introduces the eponymous auction.]

### 2. Bargaining and signaling

- Bargaining (Lectures 9 and 10)
- Signaling (Lecture 13)

#### Assignment

*Week 8*: Problem set 5, problems 1 to 3; proof (see Additional assignments): no length restrictions–although conciseness is an essential virtue in this exercise!

#### Suggested readings

- MO chapter 16 (bargaining) and chapters 10.5 to 10.9 (signaling games).
- Fudenberg, D. and J. Tirole. 1991.
*Game Theory*. MIT Press. [Chapters 9 (reputation) and 11.2 (signaling)]. - Akerlof, G. 1970. 'The Market for Lemons: Quality Uncertainty and the Market Mechanism',
*Quarterly Journal of Economics*, 84(3): 488–500. - Ambrus, A., E. Chaney and I. Salitskiy. 2016. 'Pirates of the Mediterranean: An Empirical Investigation of Bargaining with Asymmetric Information',
*Quantitative Economics*, 9(1): 217–246. - McKay, R., D. Mijovic-Prelec, and D. Prelec. 2011. 'Protesting Too Much: Self-Deception and Self-Signaling',
*Behavioral and Brain Sciences*, 34(1): 34–35. - Nash, J. 1950. 'The Bargaining Problem',
*Econometrica*, 18(2), 155–162. - Spence, M. 1973 'Job Market Signaling',
*Quarterly Journal of Economics*, 87 (1073), 355–374.