On relevant equilibria in reachability games

We study multiplayer reachability games played on a finite directed graph equipped with target sets, one for each player. In those games, it is known that there always exists Nash equilibrium. But sometimes several equilibria may coexist. For instance we can have two equilibria: first where no player reaches his set and an other all the players reach their set. It thus very natural to identify “relevant” equilibria. this paper, consider different notions of relevant including Pareto optimal high social welfare. also subgame perfect in games. provide complexity results various related decision problems both