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.
Schedule of Lectures

Lecture
Section
Topics
1
0.1 (p. 3-8), 0.1.3, 0.2, 0.3, 0.4.1
Strategic Voting, Second Price Auction, Non-cooperative, Nash Equilibrium, Cournot Duopoly
2
1.1-1.3
Trees, Nim, Strategies
3
1.4-1.5
Zermelo's Algorithm, Binary Analysis of Nim, Begin Zermelo's Theorem
4
1.7-1.9
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
2.2-2.3
Lotteries, Expectation, Game Values
7
2.4-2.5
Duel, begin Parcheesi
8
Exercises
Parcheesi, Do problems in Class (e.g. Monty Hall, ex. 2.6.26, hat problem)
9
3.1-3.2, 3.4
Preferences, Utility, Optimizing Utility
10
3.4
Von Neuman-Morgenstern Utility, examples
11
3.4-3.5
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
5.2-5.3
Convexity, Supporting Lines, Cooperative Payoff Regions, Pareto Efficiency
15
.
Midterm
16
5.4-5.5
Bargaining Sets, (Generalized) Nash Bargaining Problems and Solutions, Methods of Computation
17
5.5
Nash Axioms, Nash's Theorem and Proof
18
6.2-6.4
Minmax & Maxmin, Security Strategies, Mixed Strategies
19
6.4
Mixed Strategy Payoffs, Computing Mixed Security Strategies via Maxmin Analysis (Examples)
20
6.4-6.6
Maxmin<Minmax, Statement of Minmax Theorem, Solving Games via Separation
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 Zero-sum Games and Pareto Optimality, Correlated Equilibria
24
.
Theorem that (p1, ..., pn) is an NE iff supp(pi) is contained in imax {pi(p1, ..., pi-1, - , 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

Comments

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.
For more information, please contact Student Services, ugrad@math.ucla.edu.

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