POS 5723: Introduction to Game Theory

Syllabus

Date Topic Reading
Main text is Martin J. Osborne (2004), An Introduction to Game Theory Homework
Problems are from Osborne unless otherwise indicated

Week 1 (1/13) Introduction.
Why study game theory? Theory of rational choice. Preferences and payoff functions. Osborne, chapter 1
No homework this week.

Week 2 (1/20) Nash equilibrium I
Strategic games with ordinal preferences. Common examples (PD, BoS, etc.). Osborne, 2.1 - 2.7. Problems 16.1 18.1, 27. 2, 30.1, 31.2, and 34.2 assigned.

Week 3 (1/27) Nash equilibrium II
Best response functions. Dominated actions. Symmetric equilibria. Osborne, 2.8 - 2.10 and 3.3. Problems 42.1, 42.2, 47.1, 47.2, 74.1, and 74.2 assigned.

Week 4 (2/3) Nash equilibrium III
Randomization. vNM preferences. Mixed strategy equilibrium. Osborne 4.1 - 4.3; 4.6; 4.8; 4.10.
Recommended: A. K. Dixit & S. Skeath (2004), Games of Strategy, Chapter 5 and J. D. Morrow (1994), Game Theory for Political Scientists, pp. 81-88. Problems 114.1, 114.3, 114.4, and 141.1 assigned.
Additionally, some problems from Morrow might be assigned.

Week 5 (2/10) Rationalizability:
Iterated elimination of dominated actions. Dominance solvability. Osborne, chapter 12.
First paper due.
Problems 34.1, 387.4, 387.5, 49.1, and 391.3 assigned.

Week 6 (2/17) Extensive Form Games I
EFG with perfect information. Nash equilibrium and subgame perfect equilibrium. Finite horizon games and backwards induction. Osborne, chapter 5 and 6.3. First paper review due.
Problems 156.2, 161.1, 163.2, 173.2, and 173.4 assigned.

Week 7 (2/24) Extensive Form Games II
EFG with perfect information - extensions. Simultaneous and chance moves. Osborne, 7.1; 7.3 - 7.4; 7.6 - 7.7. Problems 211.1, 221.1, 227.3, and 234.1 assigned. (Problem session tentatively scheduled for 3/1)

Week 8 (3/3) Midterm Exam (Take-home, due March 5). None. No homework assigned this week.

Week 9 (3/17) Extensive Form Games III
Finite Bargaining Games. Osborne, 6.1 and 16.1. Morrow, pp. 145-156.
Skim: S. Golder (2006), The Logic of Pre-Electoral Coalition Formation, chapter 4.

Problems 183.3, 185.1, 185.2, and 473.1 assigned.
Additionally, some problems from Morrow might be assigned.

Week 10 (3/24) Repeated Games I
Discounting. Finitely repeated PD. Nash equilibrium and Nash equilbrium payoffs of an infinitely repeated PD. Osborne, 14.1 - 14.8. Problems 429.1, 431.1, 431.2, and 433.1 assigned.

Week 11 (3/31) Repeated Games II
Subgame perfect equilibria. One-deviation property. Folk theorems. Osborne, 14.9 - 14.12.
Morrow, chapter 9 (especially up to p. 279). Problems 439.1, 442.1, 443.1, and 445.1 assigned.
From Morrow: 9.1, 9.2, and 9.3.

Week 12 (4/7) Bayesian Games I
Strategic games with imperfect information, information sets, types, belief systems, Nash equilibrium. Osborne 9.1 - 9.3, 9.5, and 9.7.

Problems 282.1 and 284.1 assigned.

Week 13 (4/14) Bayesian Games II
Extensive games with imperfect information, Nash equilibrium, beliefs and sequential equilibrium, signaling games. Osborne 10.1 - 10.5
Skim: Clark et al. (2007), ``The Balance of Power Between Citizens and the State'' (unpublished manuscript). Focus on appendix. Second paper due.
Problems 319.3 and 331.1 assigned.

Week 14 (4/21) No class (problem session tentatively scheduled 4/19). Second paper review due.

Home Page

Date	Topic	Reading Main text is Martin J. Osborne (2004), An Introduction to Game Theory	Homework Problems are from Osborne unless otherwise indicated
Week 1 (1/13)	Introduction. Why study game theory? Theory of rational choice. Preferences and payoff functions.	Osborne, chapter 1	No homework this week.
Week 2 (1/20)	Nash equilibrium I Strategic games with ordinal preferences. Common examples (PD, BoS, etc.).	Osborne, 2.1 - 2.7.	Problems 16.1 18.1, 27. 2, 30.1, 31.2, and 34.2 assigned.
Week 3 (1/27)	Nash equilibrium II Best response functions. Dominated actions. Symmetric equilibria.	Osborne, 2.8 - 2.10 and 3.3.	Problems 42.1, 42.2, 47.1, 47.2, 74.1, and 74.2 assigned.
Week 4 (2/3)	Nash equilibrium III Randomization. vNM preferences. Mixed strategy equilibrium.	Osborne 4.1 - 4.3; 4.6; 4.8; 4.10. Recommended: A. K. Dixit & S. Skeath (2004), Games of Strategy, Chapter 5 and J. D. Morrow (1994), Game Theory for Political Scientists, pp. 81-88.	Problems 114.1, 114.3, 114.4, and 141.1 assigned. Additionally, some problems from Morrow might be assigned.
Week 5 (2/10)	Rationalizability: Iterated elimination of dominated actions. Dominance solvability.	Osborne, chapter 12.	First paper due. Problems 34.1, 387.4, 387.5, 49.1, and 391.3 assigned.
Week 6 (2/17)	Extensive Form Games I EFG with perfect information. Nash equilibrium and subgame perfect equilibrium. Finite horizon games and backwards induction.	Osborne, chapter 5 and 6.3.	First paper review due. Problems 156.2, 161.1, 163.2, 173.2, and 173.4 assigned.
Week 7 (2/24)	Extensive Form Games II EFG with perfect information - extensions. Simultaneous and chance moves.	Osborne, 7.1; 7.3 - 7.4; 7.6 - 7.7.	Problems 211.1, 221.1, 227.3, and 234.1 assigned. (Problem session tentatively scheduled for 3/1)
Week 8 (3/3)	Midterm Exam (Take-home, due March 5).	None.	No homework assigned this week.
Week 9 (3/17)	Extensive Form Games III Finite Bargaining Games.	Osborne, 6.1 and 16.1. Morrow, pp. 145-156. Skim: S. Golder (2006), The Logic of Pre-Electoral Coalition Formation, chapter 4.	Problems 183.3, 185.1, 185.2, and 473.1 assigned. Additionally, some problems from Morrow might be assigned.
Week 10 (3/24)	Repeated Games I Discounting. Finitely repeated PD. Nash equilibrium and Nash equilbrium payoffs of an infinitely repeated PD.	Osborne, 14.1 - 14.8.	Problems 429.1, 431.1, 431.2, and 433.1 assigned.
Week 11 (3/31)	Repeated Games II Subgame perfect equilibria. One-deviation property. Folk theorems.	Osborne, 14.9 - 14.12. Morrow, chapter 9 (especially up to p. 279).	Problems 439.1, 442.1, 443.1, and 445.1 assigned. From Morrow: 9.1, 9.2, and 9.3.
Week 12 (4/7)	Bayesian Games I Strategic games with imperfect information, information sets, types, belief systems, Nash equilibrium.	Osborne 9.1 - 9.3, 9.5, and 9.7.	Problems 282.1 and 284.1 assigned.
Week 13 (4/14)	Bayesian Games II Extensive games with imperfect information, Nash equilibrium, beliefs and sequential equilibrium, signaling games.	Osborne 10.1 - 10.5 Skim: Clark et al. (2007), ``The Balance of Power Between Citizens and the State'' (unpublished manuscript). Focus on appendix.	Second paper due. Problems 319.3 and 331.1 assigned.
Week 14 (4/21)	No class (problem session tentatively scheduled 4/19).		Second paper review due.