- Krasovskii Institute of Mathematics and Mechanics and Ural Federal University, Yekaterinburg, Russia
Wednesday, April 10, 2019
Abstract: The game theory studies the interaction between the agents acting to achieve their own purposes. Now the results of game theory are applied in the various fields of science. In particular, it plays the crucial role in the modern economics. I will restrict my attention to the deterministic games with complete information. I will consider non-cooperative and cooperative games. The course will consists of two parts. First one is devoted to one-shot games. In the second part I will discuss discrete-time dynamical games. I will start with the zero-sum one-short games. Here I introduce the mixed strategies and prove the existence of the solution. The natural generalization of zero-sum games are nonzero-sum games. We will consider such solution concepts as Nash equilibrium and Stackelberg solution. The cooperative one-shot game will finish the first part of the course. In the second part the main approaches to the design of solutions of dynamical games as dynamic programming and folk theorems will be introduced. Furthermore, I would like to discuss the concept of time-consistency both for non-cooperative and cooperative cases. The theoretical results will be illustrated by model examples. These examples will give an insight to optimal behaviour.