The test will cover combinatorial and zero-sum games, roughly the first two chapters of Ferguson. There will be an in-class midterm test on Thursday, October 23. November 25: Arrow Theorem: examples and the proof. November 20: An Alternative form of Shapley value. November 11: Shapley О»-transfers solution of NTU games. November 6: Cooperative games : solution for TU games, Nash solution of NTU games. November 4: Feasible solutions for cooperative games. Peres, section 4.6, Ferguson, section III.3. October 30: Proof of Nash Theorem (conclusion). October 28: Proofs of Sperner's Lemma, Brouwer fixed point theorem, and Nash Theorem. Ferguson, sections III.2.2 Peres, sections 4.2, 4.6. Ferguson, sections III.1, III.2.1 Peres, sections 4.1, 4.2. October 14: General sum games: definition, strategic and extensive form, safety levels, Nash equilibrium.

Ferguson, sections II.3.6, II.5 Peres, section 3.4. October 7: The Principle of Indifference. September 30: Proof of von Neumann Theorem. September 25: Zero-sum games: strategic form, geometric properties of the set of mixed strategies, von Neumann Theorem. Peres, sections 2.2, 3.1 Ferguson, sections II.1.1, II.1.2

Examples of using Sprague-Grundy function. September 16: The games of Nim and misere Nim. Peres, section 2.1 Ferguson, sections I.1, I.2. Other topics will include the coalition games and Shapley value, applications of Game theory to voting (such as Arrow theorem), auctions, and stochastic games. The next big topic will be the general sum games and Nash equilibrium. We will discuss various methods for solving such games. After a brief discussion of partisan combinatorial games, we will discuss the zero-sum games and von Neuman's minimax theorem. The course will start with the discussion of impartial combinatorial games: subtraction game, Nim, and Chomp, will discuss the Sprague-Grundy value. The course will discuss the mathematical aspects of the game theory, an important area of Mathematics/Probability with multiple applications to Economics, Political Science, and Evolutionary Biology, to name a few.

If a student believes that s/he does have the necessary background material, and is able to prove it (e.g., has a transfer credit from a different university), then s/he should submit a 'Prerequisite/Corequisite Waiver Request Form'. Prerequisites will be checked, and students not meeting them will be removed from the course by the end of the second week of classes. Teaching Assistant: Charles Tsang ( Hours: by appointment. MAT406H5F Mathematical Introduction to Game TheoryД¬lass Location & Time: Tue, 11:00 AM - 12:00 PM and Thu, 01:00 PM - 03:00 PM DV 1104

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