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

Week 2 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.

Week 3 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.

Week 4 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.
Additionally, some problems from Morrow might be assigned.

Week 5 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

Week 6 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.

Week 7 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.

Week 8 Extensive Form Games III
Finite Bargaining Games. Osborne, 6.1 and 16.1.
S. Golder (2006), The Logic of Pre-Electoral Coalition Formation, chapter 4.
Recommended: Morrow, pp. 145-156.
Problems 183.3, 185.1, 185.2, and 473.1.
Additionally, some problems from Morrow might be assigned.

Week 9 Midterm Exam. None. No homework this week.

Week 10 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.

Week 11 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.
From Morrow: 9.1, 9.2, and 9.3.

Week 12 No class - MPSA conference. None. No homework this week.

Week 13 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.
Second paper due.
Problems 282.1 and 284.1.

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 (2007), ``The Balance of Power Between Citizens and the State'' (unpublished manuscript).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

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	Introduction. Why study game theory? Theory of rational choice. Preferences and payoff functions.	Osborne, chapter 1	No homework this week.
Week 2	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.
Week 3	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.
Week 4	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. Additionally, some problems from Morrow might be assigned.
Week 5	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
Week 6	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.
Week 7	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.
Week 8	Extensive Form Games III Finite Bargaining Games.	Osborne, 6.1 and 16.1. S. Golder (2006), The Logic of Pre-Electoral Coalition Formation, chapter 4. Recommended: Morrow, pp. 145-156.	Problems 183.3, 185.1, 185.2, and 473.1. Additionally, some problems from Morrow might be assigned.
Week 9	Midterm Exam.	None.	No homework this week.
Week 10	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.
Week 11	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. From Morrow: 9.1, 9.2, and 9.3.
Week 12	No class - MPSA conference.	None.	No homework this week.
Week 13	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.	Second paper due. Problems 282.1 and 284.1.
Week 14	Bayesian Games II Extensive games with imperfect information, Nash equilibrium, beliefs and sequential equilibrium, signaling games.	Osborne 10.1 - 10.5 Recommended: Clark et al. (2007), ``The Balance of Power Between Citizens and the State'' (unpublished manuscript). Focus on appendix.	Second paper review due. Problems 319.3 and 331.1.