Associated consistency and the Aumann-Drèze value

Florian Navarro

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Abstract: 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.

Keywords: game theory; cooperative games; coalition structures; associated consistency; shapley value; aumann-drèze value (search for similar items in EconPapers)
Date: 2022
Note: View the original document on HAL open archive server: https://univ-angers.hal.science/hal-03678064v1
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Published in International Game Theory Review, inPress, ⟨10.1142/S0219198922500189⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03678064

DOI: 10.1142/S0219198922500189

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