### November 25, 2019

**Marie Van Den Bogaard**(ULB )

In this talk, we consider multiplayer games on graphs. In such games, each player has his own objective, that does not necessarily clash with the objectives of the other players. In this “non zero-sum” context, equilibria are a better suited solution concept than the classical winning strategy notion. We will focus on a refinement of the well-known Nash Equilibrium concept: Subgame Perfect Equilibrium (SPE for short), where players have to play rationnally in every scenario, even the one deviating from the planned outcome. We will explain why this refinement is a relevant solution concept in multiplayer games and show how to handle them in reachability games, both in the qualitative and quantitative setting.