Before revision:  {\em   The core is a key solution concept in cooperative game theory.
After revision:  Next, we provide new insights showing how discerning core imputations of an assignment games are by studying them via the lens of complementary slackness. We present a relationship between the competitiveness of individuals and teams of agents and the amount of profit they accrue in imputations that lie in the core, where by{\em The core is a key solution concept in cooperative game theory.