Values for environments with externalities – The average approach

Abstract

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On the least square prenucleolus for games with externalities

“…Since that the least square prenucleolus of a game with externalities is the weighted least square prenucleolus of the TU game of [2], the fulfilment of the remaining properties is plain from the properties that [11] prove for the latter. This is an immediate consequence of Theorem 10 in [7]. ◻…”

“…Specifically, this new value for games with externalities can be interpreted as the weighted least square prenucleolus for the TU game in [2], that is built using an "average approach" (cf. [7]). A consistency property has been formalized to characterize the family of weigthed least square values for TU games studied in [10] and in [11].…”

“…Next, we complete the previous list by adding the properties of strong symmetry and of coalitional monotonicity on , that are originally introduced in [7].…”

“…Considering all the comments above, the analysis of the properties that LS E -prenucleolus satisfy readily follows. For this purpose, we largely use the ideas in [7] about properties to satisfy those solutions for externalities games that are obtained from solutions for TU games using an "average approach".…”

Modelling Coalitions: From Concept Formation to Tailoring Empirical Explanations

“…Another example of this conceptual venue of research is the introduction of externalities to the Shapley value model of coalitional games via stochastic approaches [56] and methods for sharing externalities [57]. Further developments have addressed the linearity assumption entailed in the Shapley-Shubik value, adjusting the original conceptual model to incorporate non-linearities [58].…”