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.

我们研究了在配有目标集的有限有向图上玩的多人可及性游戏，每位玩家一个。在那些可达性博弈中，众所周知总是存在纳什均衡。但是有时可能会存在几种均衡。例如，我们可以有两个平衡点：第一个平衡点，没有玩家达到其目标集，而另一个平衡点，所有玩家都达到其目标集。因此，确定“相关”均衡是很自然的。在本文中，我们考虑了相关的纳什均衡的不同概念，包括帕累托最优均衡和具有较高社会福利的均衡。我们还研究了可达性游戏中的相关子游戏完美平衡。我们为纳什均衡和子博弈完美均衡提供了各种相关决策问题的复杂性结果。