Flow methods for cooperative games with generalized coalition configuration

Encarnación Algaba (), Eric Rémila () and Philippe Solal ()
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Encarnación Algaba: IMUS - Matematica Aplicada II and Instituto de Matematicas de la Universidad de Sevilla (IMUS), Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n, 41092 Sevilla, Spain
Eric Rémila: GATE-LSE - Université de Saint-Etienne, UMR CNRS GATE Lyon-St-Etienne UMR 5824, F-42023 Saint- Etienne Institution GATE-LSEFrance
Philippe Solal: GATE-LSE - Université de Saint-Etienne, UMR CNRS GATE Lyon-St-Etienne UMR 5824, F-42023 Saint- Etienne

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Abstract: A cooperative games with a coalition structure is formed by a TUgame and a partition of the agent set. For this class of games, the Owen value is computed as a two-step procedure where the relevant coalitions are those formed by the union of some elements of the partition and a coalition of another element of the partition. In this paper, we consider a broader class of games where the partition is replaced by a collection of (not necessarily pairwise disjoint) coalitions over the agent set and where, in each element of this collection, cooperation among the agents is restricted. Agents then organize themselves into a profile of feasible coalitions. This class of games can be applied to several situations such as the problem of allocating aircraft landing fees in the presence of airlines and codeshare flights. We begin by defining and axiomatically characterizing the class of flow methods, which are marginal values whose coefficients induce a unit flow on the graph of feasible coalition profiles. We then define Owen-type values constructed from flow methods. We show that these values are flow methods whose flow is decomposable into two flows. Finally, we introduce two axioms from which we characterize the flows that can be decomposed in this way, and hence the flow methods constructed by our Owen-type procedure. The last part of the paper studies some special cases.

Keywords: Coalition configuration Cooperative games Flow Set systems Marginalist values Airport games Mathematics Subject Classification (2000) 91A12 91A43 05C21; Coalition configuration; Cooperative games; Flow; Set systems; Marginalist values; Airport games Mathematics Subject Classification (2000) 91A12; 91A43; 05C21 (search for similar items in EconPapers)
Date: 2025
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-05164853v1
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Published in Journal of Optimization Theory and Applications, inPress, ⟨10.1007/s10957-025-02780-8⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-05164853

DOI: 10.1007/s10957-025-02780-8

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