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 
0.1 (p. 38), 0.1.3, 0.2, 0.3, 0.4.1 
Strategic Voting, Second Price Auction, Noncooperative, Nash Equilibrium, Cournot Duopoly 
2 
1.11.3 
Trees, Nim, Strategies 
3 
1.41.5 
Zermelo's Algorithm, Binary Analysis of Nim, Begin Zermelo's Theorem 
4 
1.71.9 
Zermelo's Theorem, Chess, Value of a Strictly Competitive Game, Subgame Perfect Equilibrium, Team Games, etc. 
5 
2.1 
Review of Probability, Bayes Rule 
6 
2.22.3 
Lotteries, Expectation, Game Values 
7 
2.42.5 
Duel, begin Parcheesi 
8 
Exercises 
Parcheesi, Do problems in Class (e.g. Monty Hall, ex. 2.6.26, hat problem) 
9 
3.13.2, 3.4 
Preferences, Utility, Optimizing Utility 
10 
3.4 
Von NeumanMorgenstern Utility, examples 
11 
3.43.5 
St. Petersburg Paradox, Risk Averse, Risk Loving 
12 
4.1 
Payoff Functions via Expectation; Strategic Form of Duel, Bimatrices, Finding Pure Strategy NE's 
13 
4.6 
Domination 
14 
5.25.3 
Convexity, Supporting Lines, Cooperative Payoff Regions, Pareto Efficiency 
15 
Midterm 

16 
5.45.5 
Bargaining Sets, (Generalized) Nash Bargaining Problems and Solutions, Methods of Computation 
17 
5.5 
Nash Axioms, Nash's Theorem and Proof 
18 
6.26.4 
Minmax & Maxmin, Security Strategies, Mixed Strategies 
19 
6.4 
Mixed Strategy Payoffs, Computing Mixed Security Strategies via Maxmin Analysis (Examples) 
20 
6.46.6 
Maxmin 
21 
6.7 or 6.8 
Battleships or Inspection 
22 
7.1 
Best Response (=Reaction Curve) Analysis of Bimatrix Games, Prisoner's Dilemma & Chicken 
23 
7.2 
Relation of NE's to Maxmin Solutions of Associated Zerosum Games and Pareto Optimality, Correlated Equilibria 
24 
Theorem that (p1, ..., pn) is an NE iff supp(pi) is contained in imax {pi(p1, ..., pi1,  , pi+1, ..., pn)} for all i. Methods of computing Nash equilibria (2 player 2x3, 3x3 cases) 

25 
Computations, Word problems 

26 
7.2 
Duopoly (Cournot, Stackelberg), Oligopoly, Perfect Competition 
27 
7.7 
Sketch of Proof of Existence of NE 
28 
Review 