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We address the problem of the division of a homogeneous, infinitely divisible good among a set of agents when several characteristics have to be taken into account. Specifically, we extend the classic random arrival rule to division problems which do not necessarily represent a bankruptcy situation, and in which several references are considered for each agent. We establish the links of the extended rule with the classic random arrival rule and we prove that the outcomes coincide with the Shapley value of an appropriate cooperative game. The results permit a complete description of the allocations that would be obtained for any value of the quantity to be divided.

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