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The main goal of this paper is to shed light on economic allocation problems, in particular by focusing on individuals who receive nothing –i.e. a zero allocation or payoff –. It is worth noting that, in certain contexts, such individuals may be considered as poor or socially excluded. To this end, our study relies on the notion of cooperative games with transferable utility and we consider the Linear Efficient and Symmetric values – called LES values – as allocation rules. Null players in the sense of Shapley are extensively studied. The analysis is facilitated by two parametric representations of the family of values, two broader classes of Null players are introduced. We clearly show that any LES value can be characterized in two different ways using the axioms based on the two types of null players. Several characterizations of subclasses of LES values are given using our approach.
