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Article Dans Une Revue International Game Theory Review Année : 2022

Associated consistency and the Aumann-Drèze value

Résumé

This article presents an axiomatic characterization of the Aumann-Drèze value (1974) for cooperative games with coalition structures. We build an associated game that extends the original associated game presented by Hamiache (2001) to cooperative games with coalition structures. We use a similar approach to the one used in Hamiache and Navarro (2020). This new associated game is expressed through a matrix form. We show that the series of successive associated games is convergent and that its limit is an inessential game. This allows us to propose a characterization of the Aumann-Drèze value that relies on associated consistency, inessential game and continuity axioms. Hence, this paper strengthens the results of Hamiache (2001) and Hamiache and Navarro (2020) considering that if these axioms are viewed as desirable, we are now able to provide a unique value for three different types of problems : the Shapley value on standard games (Hamiache 2001), the Hamiache-Navarro value on games with graphs (Hamiache and Navarro 2020) and the Aumann-Drèze value for games with coalition structures.
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Dates et versions

hal-03678064 , version 1 (25-05-2022)

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Florian Navarro. Associated consistency and the Aumann-Drèze value. International Game Theory Review, In press, ⟨10.1142/S0219198922500189⟩. ⟨hal-03678064⟩

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