The proportional Shapley value and an application

Sylvain Béal (1) , Eric Rémila (2) , Philippe Solal (2) , Sylvain Ferrières (1)

1 CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190)
2 GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne

We introduce a non linear weighted Shapley value for cooperative games with transferable utility, in which the weights are endogenously given by the players' stand-alone worths. We call it the proportional Shapley value since it distributes the Harsanyi dividend (Harsanyi, 1959) of all coalitions in proportion to the stand-alone worths of its members. We show that this value recommends an appealing payoff distribution in a land production economy introduced in Shapley and Shubik (1967). Although the proportional Shapley value does not satisfy the classical axioms of linearity and consistency (Hart and Mas-Colell, 1989), the main results provide comparable axiomatic characterizations of our value and the Shapley value by means of weak versions of these two axioms. Moreover, our value inherits several well-known properties of the weighted Shapley values.

Mots clés: (Weighted) Shapley value; proportionality; Harsanyi dividends; land production economy; potential

Domaines: Informatique et théorie des jeux [cs.GT]; Microstructure des marchés [q-fin.TR]

Sylvain Béal, Eric Rémila, Philippe Solal, Sylvain Ferrières. The proportional Shapley value and an application . 2016. ⟨hal-01362228⟩