On relevant equilibria in reachability games

Abstract

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