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Math 167: General Course Outline

Catalog 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

2.2-2.3

Make eplicit definitios in 2x2 case and minmax. Minmax Statement

3

2.4

Solving 0-sum 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 non-cooperative (aka general sum) game

12

4.1

Basic 2 x 2 examples (PD, Dove-Hawk, 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)
Midterm 2

25

Price of Anarchy, Chapter 8

26

27

Stable matching, Chapter 10

28

Review