Joint dominance of payoff vectors ($u^{\prime }\ge u,u^{\prime }\ne u$)

A feasible payoff vector $u^{\prime }$ jointly dominates $u$ if every coordinate is at least as large and at least one is strictly larger. A Pareto optimal vector has no feasible joint dominator. Strict increase of every coordinate is not required. This compares each player's own utilities, not the numerical size of utilities across different players.