Fractional Combinatorial Two-Player Games

We propose a fractional relaxation of two-player combinatorial games. Two players can move or/and add fractions of tokens on the nodes of a graph and a player wins if he is the first one to reach a configuration in some specified set. Both allowed moves and winning configurations are defined thanks to linear inequalities. Our framework applies to many two-players games including the fractional variant of cops and robber games. We give some results and promising perspectives of this new framework. Joint work with F. Giroire, S. Pérennes, R.P. Soares.