The paper introduces the Union Shapley Value for assessing groups in coalitional games using sequential elimination, proves its order-independence for most semivalues, and distinguishes total worth from synergy in group values.
The Shapley group value
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abstract
Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person interaction situation, we propose a group value, which we call the Shapley group value, as a priori evaluation of the prospects of a group of players in a coalitional game when acting as a unit. We study its properties and we give an axiomatic characterization. Relaying on this valuation we analyze the profitability of a group. We motivate our proposal by means of some relevant applications of the Shapley group value, when it is used as an objective function by a decisionmaker who is trying to identify an optimal group of agents in a framework in which agents interact and the attained benefit can be modeled bymeans of a transferable utility game. As an illustrative examplewe analyze the problem of identifying the set of key agents in a terrorist network.
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Sequential Elimination and Union Shapley Value for Group Assessment in Coalitional Games
The paper introduces the Union Shapley Value for assessing groups in coalitional games using sequential elimination, proves its order-independence for most semivalues, and distinguishes total worth from synergy in group values.