Stochastic two-player games on directed graphs are widely used for modeling and analysis of discrete systems operating in an unknown (adversarial) environment. Possible configurations of a system and its environment are represented as vertices...

**Stochastic two-player games** on directed graphs are widely used for **modeling and analysis of discrete systems operating in an unknown** (adversarial) environment. Possible configurations of a system and its environment are represented as vertices, and the transitions correspond to actions of the system, its environment, or "nature". A run of the system then corresponds to an infinite path in the graph. Thus, a system and its environment can be seen as two players with antagonistic objectives, where one player (the system) aims at maximizing the probability of "good" runs, while the other player (the environment) aims at the opposite.

In many cases, there exists an equilibrium value of this probability, but optimal strategies for both players may not exist.

We introduce **basic concepts and algorithmic questions** studied in this area, and we **mention some long-standing open problems**. Then, we mention **selected recent results**.

Prof. RNDr. Antonín Kučera, Ph.D., is an internationally recognized researcher in theoretical computer science. He works in the areas at the intersection of mathematical logic and theoretical computer science such as formal modelling and verification of infinite-state systems, questions of decidability and complexity of analysis of models over various classes of such systems, use of modal and temporal logics. He also studies stochastic systems, game theory and its applications in the areas above. He is a full professor and the head of the Institute for Theoretical Computer Science at Faculty of Informatics, Masaryk University, Brno. His group belongs among the top centers of Czech computer science, he advises a number of PhD. students; some of his past students are themselves recognized scientists.

Its **program** consists of a **one-hour lecture** followed by a **discussion**. The lecture is based on an (internationally) exceptional or remarkable achievement of the lecturer, presented in a way which is comprehensible and interesting to a broad computer science community. The lectures are in English.

**The seminar** is organized by the organizational committee consisting of Roman Barták (Charles University, Faculty of Mathematics and Physics), Jaroslav Hlinka (Czech Academy of Sciences, Computer Science Institute), Michal Chytil, Pavel Kordík (CTU in Prague, Faculty of Information Technologies), Michal Koucký (Charles University, Faculty of Mathematics and Physics), Jan Kybic (CTU in Prague, Faculty of Electrical Engineering), Michal Pěchouček (CTU in Prague, Faculty of Electrical Engineering), Jiří Sgall (Charles University, Faculty of Mathematics and Physics), Vojtěch Svátek (University of Economics, Faculty of Informatics and Statistics), Michal Šorel (Czech Academy of Sciences, Institute of Information Theory and Automation), Tomáš Werner (CTU in Prague, Faculty of Electrical Engineering), and Filip Železný (CTU in Prague, Faculty of Electrical Engineering)

**The idea to organize this seminar** emerged in discussions of the representatives of several research institutes on how to avoid the undesired fragmentation of the Czech computer science community.