“…Formally, each player i has a subset of states S i as their safe states, and gets a payoff 1 if the play never leaves the set S i and gets payoff 0 otherwise. This result was generalized to general state and action spaces [23,15], where only -equilibria exist. However, not much more is known: for example, the existence of -Nash equilibria when the payoff for each player is given by an open set ("reachability games") remained open.…”