Minicourse 1: Topics in Game theory
1. Matrix, bimatrix, and n-person games in normal form; solving in pure and mixed strategies.
2. Nash equilibrium (NE) in pure strategies for n-person games in normal and positional form. Nash-solvabile and tight game forms.
3. On minimal and locally minimal NE-free bimatrix games.
4. Domination of strategies and dominance equilibrium (DE).
5. On Acyclicity, Nash- and Dominance-solvability of games and game forms.
6. Effectivity Functions in Game, Voting, and Graph Theories.
7. Characterizing Normal Forms of Positional Games and Read-Once Boolean Functions.
8. Impartial games; Sprague-Grundy theory
No Prerequisites. Knowledge of basic concepts of Linear Programming and Graph Theory would be useful, but everything will be explained in class. We will cover four or five from the above 8 topics: the first two and two or three more, it will depend on students' preference and level.
Minicourse 2: The history of combinatorics
Lectures 1 and 2: Ancient and renaissance combinatorics