 If these conditions all obtain the argument for dilemma goes through as before. Defection strictly dominates cooperation for each player, and \((\bC,\bC)\) is strictly preferred by each to \((\bD,\bD)\). If one of the two \(\gt\) signs in each of the conditions \(a\)–\(c\) is replaced by a weak inequality sign (\(\ge\)) we have a weak PD. \(\bD\) weakly dominates \(\bC\) for each player (i.e., \(\bD\) is as good as \(\bC\) in all cases and better in some) and \((\bC,\bC)\) weakly better than \((\bD,\bD)\) (i.e., it is at least as good for both players and better for one). Since none of the clauses requires comparisons between \(r\)'s payoffs and \(c\)'s, we need not assume that \(\gt\) has any “interpersonal” significance.