 Best response moves are the main ingredient for game equilibria. Formally, a Nash equilibrium is a strategy profile, fixing a unique choice for each player, where nobody can improve by unilaterally changing strategy when all others maintain theirs. There are several ways of defining this property in extended modal preference languages. One possibility is to simply introduce a new atom \(b_i\), stating that the current world is the best player i could have achieved in light of the opponents’ actions. In this language, Nash equilibrium are characterized by 