Mini-Workshop: Positional Games

Abstract

The theory of Positional Games is a branch of Combinatorics, whose main aim is to develop systematically an extensive mathematical basis for a variety of two player perfect information games, ranging from such commonly popular games as Tic-Tac-Toe and Hex to purely abstract games played on graphs and hypergraphs. Though a close relative of the classical Game Theory of von Neumann and of Nim-like games popularized by Conway and others, Positional Games are quite different and are of much more combinatorial nature. The first papers on the subject appeared in the 60's and the 70's. J\'ozsef Beck turned it into a well established mathematical discipline through a series of papers spanning the last quarter century. Positional games are strongly related to several other branches of Combinatorics like Ramsey Theory, Extremal Graph and Set Theory, the Probabilistic Method. The subject has proven to be quite instrumental in deriving important results in Theoretical Computer Science, in particular in derandomization and algorithmization of important probabilistic tools. Recently the field of Positional Games has been experiencing an explosive growth with quite a few new and important results in different directions (new versions of game definitions; analysis of biased games; exact results in Ramsey-type games; games of geometric nature; fast winning strategies etc.) appearing. The purpose of this mini-workshop was two-fold: it was aimed to provide an opportunity for leading researchers in the field to present and discuss their recent results on a systematic basis; it was also meant to attract new researchers, including students, to this exciting and rapidly developing field. 17 scientists from different countries participated in the meeting. The organizers and participants would like to thank the Mathematisches Forschungsinstitut Oberwolfach for providing an inspiring setting for this event.