An Index of Unfairness

The Shapley distance is introduced as a measure of the extent to which output sharing among the stakeholders of an organization can be considered unfair. In fact, it measures the distance between an arbitrary pay profile and the Shapley pay profile under a given technology, the latter profile defining the fair distribution. Therefore, this chapter contributes to the literature that studies economic inequality using game theory. In particular, we provide an axiomatic characterization to a notion of unfairness, namely the Shapley distance, and show that it can be used to determine the outcome of an underlying bargaining process. We also present applications highlighting how favoritism in income distribution, egalitarianism, and taxation violate the different ideals of justice that define the Shapley value and how unfairness can be further unbundled to determine its origins. The analysis has implications that can be tested using real-world data sets

On some decisive players for linear efficient and symmetric values in cooperative games with transferable utility

The main goal of the paper is to shed light on economic allocations issues, in particular by focusing on individuals who receive nothing (that is an amount of zero allocation or payoff). It is worth noting that such individuals may be considered, in some contexts, as poor or socially excluded. To this end, our study relies on the notion of cooperative games with transferable utility and the Linear Efficient and Symmetric values (called LES values) are considered as allocation rules. Null players in Shapley sense are extensively studied ; two broader classes of null players are introduced. The analysis is facilitated by the help of a parametric representation of LES values. It is clearly shown that the control of what a LES value assigns as payoffs to null players gives significant information about the characterization of the value. Several axiomatic characterizations of subclasses of LES values are provided using our approach

On some decisive players for linear efficient and symmetric values in cooperative games with transferable utility

The main goal of the paper is to shed light on economic allocations issues, in particular by focusing on individuals who receive nothing (that is an amount of zero allocation or payoff). It is worth noting that such individuals may be considered, in some contexts, as poor or socially excluded. To this end, our study relies on the notion of cooperative games with transferable utility and the Linear Efficient and Symmetric values (called LES values) are considered as allocation rules. Null players in Shapley sense are extensively studied ; two broader classes of null players are introduced. The analysis is facilitated by the help of a parametric representation of LES values. It is clearly shown that the control of what a LES value assigns as payoffs to null players gives significant information about the characterization of the value. Several axiomatic characterizations of subclasses of LES values are provided using our approach