Pareto improvement ($u_i(a^{\prime })\ge u_i(a)\forall i,u_j(a^{\prime })>u_j(a)\text{for some }j$)

A feasible change weakly increasing every participant's utility and strictly increasing at least one. An assignment is Pareto optimal exactly when no Pareto improvement exists. This comparison permits coordinated changes by several participants; it is different from a profitable unilateral deviation used to test a Nash equilibrium.