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Associated Consistency and the Aumann–Drèze Value

机译：Associated Consistency and the Aumann–Drèze Value

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This paper presents an axiomatic characterization of the Aumann–Drèze value Aumann, R. J. and Drèze, J. H. 1974 Cooperative games with coalition structures, Int. J. Game Theory 3, 217–237 for cooperative games with coalition structures. We build an associated game that extends the original associated game presented by Hamiache 2001 Associated consistency and Shapley value, Int. J. Game Theory 30, 279–289 to cooperative games with coalition structures. We use a similar approach to the one used in Hamiache and Navarro 2020 Associated consistency, value and graphs, Int. J. Game Theory 49, 227–249. 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 Associated consistency and Shapley value, Int. J. Game Theory 30, 279–289 and Hamiache and Navarro 2020 Associated consistency, value and graphs, Int. J. Game Theory 49, 227–249 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, G. 2001 Associated consistency and Shapley value, Int. J. Game Theory 30, 279–289, the Hamiache–Navarro value on games with graphs Hamiache, G. and Navarro, F. 2020 Associated consistency, value and graphs, Int. J. Game Theory 49, 227–249 and the Aumann–Drèze value for games with coalition structures.

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