Minicourse 1:  Topics in Game theory

Lecturer: Vladimir Alexander Gurvich,  Rutgers University, NJ, USA and National Research University, Higher School of Economics, Moscow, Russia.

Abstract: 

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.

Download:

Description and references, Slides 1, Slides 2, Slides 3, Slides 4, Slides 5, Slides 6, Slides 7, Slides 8, Slides 9, Slides 10, Slides 11, Slides 12.

 

Minicourse 2: The history of combinatorics

Lecturer: Robin Wilson, Open University, London, UK

Abstract:

Lectures 1 and 2:  Ancient and renaissance combinatorics
Lectures 3 and 4: The combinatorics of Leonhard Euler
Lectures 5 and 6: 150 years of colouring problems in graph theory
Lectures 7 and 8: Miscellaneous topics (the history of designs; 20th-century graph theory, etc.)

Download slides: Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7 and 8