Jarosław Pykacz (Institute of Mathematics, University of Gdańsk, Poland)
Guest researcher at our institute (April – May, 2019)
Talk summary: The idea of a solution concept of a game that nowadays is called Berge equilibrium (BE) was launched by French mathematician Claude Berge in his book published in 1957, i. e. seven years after John Nash introduced his concept of equilibrium of a game. The idea of BE is in a sense opposite to the idea of Nash equilibrium (NE). While NE is based on egoism: each player aims to maximize his own payoff, BE is based on altruism: each player’s aim is to maximize payoffs of all the other players, so when every player does so, everyone is better off.
However, while NE quickly became very popular (the number of papers devoted to NE surely is counted in thousands), the concept of BE was almost forgotten and only recently regains popularity. Actually, BE was not completely forgotten mostly because Berge’s book was translated into Russian where a small group of mathematicians continued working on this concept. However, they published their papers in Russian, usually in local journal, so these papers remained unknown in the English-speaking world.
Fortunately, at that time numerous foreign students, mostly from Arabic countries, studied in the Soviet Union. Some of them wrote PhD theses on BE and after returning to their homelands continued working on BE. In this way the concept of BE was restored to the world’s science.
Nevertheless, the number of papers devoted to BE is still very small (probably does not exceed 50) and there are still numerous open problems concerning this concept. In my talk I shall present some of them. I shall also talk about my and my student’s achievements in this area.
In the beginning of the talk I shall introduce basic necessary notions from game theory, so the talk will be understandable even for complete laymen in this area.