A Computational Test for the Existence of a Monotonic Core Payoff Configuration

The objects of study In this paper are transferable utility games and prescriptions for such games In the form of an array of outcomes for all coalitions or payoff configurations. We aim to identify a necessary and sufficient condition on games for the existence of a payoff configuration which is a core allocation and also satisfies an equity requirement named population monotonicity. Unlike the conditions found In the previous literature. we identify an 'operational' condition: given a game. its zero-normalization is non-negative and the value of the objective junction in the linear programming problem associated with the game is zero at its solution.