Math 167: General Course Outline
Course Description
167. Mathematical Game Theory. (4) Lecture, three hours; discussion, one hour. Requisite: course 115A. Quantitative modeling of strategic interaction. Topics include extensive and normal form games, background probability, lotteries, mixed strategies, pure and mixed Nash equilibria and refinements, bargaining; emphasis on economic examples. Optional topics include repeated games and evolutionary game theory. P/NP or letter grading.
Outline update: D. Blasius, 5/02
NOTE: While this outline includes only one midterm, it is strongly recommended that the instructor considers giving two. It is difficult to schedule a second midterm late in the quarter if it was not announced at the beginning of the course.
Schedule of Lectures
Lecture  Section  Topics 

1 
2.1 
Example and graphical solution 
2 
2.22.3 
Make eplicit definitios in 2x2 case and minmax. Minmax Statement 
3 
2.4 
Solving 0sum games. 
4 
2.4 
2.4 Continued 
5 
2.5 
Nash equilibria (mutual best responses) 
6 
2.6 
Proof of minmax: assume separating hyperplane theorem and derive proof. Do planar n by 2 case first with pictures. 
7 
Prove separating hyperplanes 

8 
Work on good problems in class 

9 
3.1 
Work on 3.1 material 
10 
3.2 
Work on 3.2 material 
11 
3.2 
Introduce noncooperative (aka general sum) game 
12 
4.1 
Basic 2 x 2 examples (PD, DoveHawk, etc.) 
13 
4.2 
Solve two player NE's (2x2, 3x3 case) 
14 
Review for Midterm 

15 
Midterm 

16 
4.3 
Many player NE's 
17 
4.3 
Many player NE's (cont.) 
18 
4.4 
Potential games 
19 
4.5 
Tragedy of the Commons. 
20 
Beginning of proof of NE's: definition of a convex correspondence. 

21 

22 
7.1 
Proof NE's exist based on Kakutani (convex correspondences have fixed points) 
23 
7.2 
Review for Midterm 
24 
Midterm 2 (L13) 

25 
Price of Anarchy, Chapter 8 

26 

27 
Stable matching, Chapter 10 

28 
Review 