Say I am player $i$ in an $n$-player normal-form game. Let $s_{-i}$ denote the strategies selected by the remaining players. Let $s_{i}$ denote my chosen strategy. Assume that
$$ u_{i}(s_{i}, s_{-i}) = C_{s_{-i}} \quad \forall s_{i} $$
That is, given the opposing strategies $s_{-i}$, my utility is equal to a constant $C_{s_{-i}}$ (which implicitly depends on the strategies $s_{-i}$ chosen by other players) regardless of the strategy $s_{i}$ that I choose to play. Say that this condition holds for all other players as well (that is for all $i$). Is there a name for this type of a game? I suppose this is equivalent to saying that all pure strategy profiles are pure Nash equilibria.