STAT 155: Game Theory
Lecture Schedule
The section numbers given here are from the two text books. Ferguson is "F" and Karlin and Peres is "KP".
Please note that this is just a guide and may change as the semester progress.The web-page will be updated
accordingly.
- Week-1,2: (08/30 - 09/06)
- Fri: Course policy, Introduction and examples.
- Mon: Labor Day (holiday).
- Wed: Introduction and examples (continued).
- Fri: Impartial Combinatorial Games, a simple Take-Away Game (F Section 1.1.1).
- Week-3: (09/09 - 09/13)
- Mon: Combinatorial Games, P and N positions (F Sections 1.1.2 and 1.1.3).
- Wed: Subtraction Games, examples (F Section 1.1.5).
- Fri: Subtraction Games, examples continued (F Section 1.1.5).
- Week-4: (09/16 - 09/20)
- Mon: The Game of Nim, Nim sum, Bouton's Theorem (F Sections 1.2.1, 1.2.2 and 1.2.3).
- Wed: Proof of Bouton's Theorem, The Game Nimble (F Sections 1.2.4 and 1.2.6).
- Fri: The Staircase Nim, The Game of Rims (F Section 1.2.6 and KP Example 10.1.13).
- Week-5: (09/23 - 09/27)
- Mon: The Game of Rims (continued), Turning Turtles
(KP Example 10.1.13 and F Section 1.2.6).
- Wed: Sum of two combinatorial games, examples, definition of equivalence
(KP Section 10.1.3).
- Fri: Properties of equivalence and examples (KP Section 10.1.3).
- Week-6: (09/30 - 10/04)
- Mon: Definition of Sprague-Grundy function, examples,
Sprague-Grundy Theorem (KP Section 10.1.3).
- Wed: Proof of Sprague-Grundy Theorem, Sum Theorem and proof
(KP Section 10.1.3).
- Fri: The Game of Green Hackenbush (KP Example 10.1.35).
- Week-7: (10/07 - 10/11)
- Mon: Two-Person Zero-Sum Games, examples (KP Section 2.1).
- Wed: Pure and mixed strategies (F Sections 2.1.1. 2.1.2 and 2.1.3).
- Fri: von Neumann's Minimax Theorem, applications (F Section 2.1.4).
- Week-8: (10/14 - 10/18)
- Mon: Matrix Games, Saddle Points, Examples (F Section 2.2.1 and KP Section 2.3)
- Wed: Nash Equilibrium (KP Section 2.3).
- Fri: Solutions of all 2 x 2 Matrix Games (F Section 2.2.2).
- Week-9: (10/21 - 10/25)
- Mon: Review for the Midterm Examination.
- Wed: Midterm.
- Fri: Dominated strategies, Solving 2 x n and m x 2 Games
(F Sections 2.2.3 and 2.2.4 and KP Sections 2.4.1 and 2.4.2)
- Week-10: (10/28 - 11/01)
- Mon: Solving games with non-singular, diagonal and triangular pay-off matrix.
(F Sections 2.3.2, 2.3.3 and 2.3.4).
- Wed: Solving games with symmetries
(F Sections 2.3.5 and 2.3.6 and KP Sections 2.4.3).
- Fri: Solving general finite games, upper and lower values (F Sections 2.4.1 and 2.4.2)
- Week-11: (11/04 - 11/08)
- Mon: Pivot Method for solving games (F Section 2.4.5).
- Wed: Numerical example of solving by pivot method (F Section 2.4.6).
- Fri: Relation with linear programming, basics of linear programming
(F Section 2.4.4 and KP Section 2.7.1).
- Week-12: (11/11 - 11/15)
- Mon: Veterens Day (holiday).
- Wed: Two-Person Zero-Sum Games with infinite action spaces (KP Section 2.8).
- Fri: Two-Person General Sum Games, examples (KP Section 3.1).
- Week-13: (11/18 - 11/22)
- Mon: Nash's Equilibrium, examples (KP Section 3.2).
- Wed: General-sum games with more than two players, examples (KP Section 3.3).
- Fri: Pure and mixed Nash Equilibrium, Nash's Theorem (KP Section 3.3).
- Week-14: (11/25 - 11/29)
- Mon: Potential games, the game of coloring of a graph (KP Section 3.6).
- Wed: The game of coloring of a graph continued (KP Example 3.6.4).
- Fri: Thanks Giving Holiday.
- Week-15: (12/02 - 12/06)
- Mon: Theory of Social Choice, voting and ranking mechanisms, examples
(KP Section 5.1).
- Wed: Arrow’s Impossibility Theorem (KP Section 5.2).
- Fri: Applications of Arrow's Impossibility Theorem (KP Section 5.3).