On the Internal and External Stability of Coalitions and Application to Group Purchasing Organizations

Dongshuang Hou, Aymeric Lardon and Hao Sun
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Dongshuang Hou: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China
Hao Sun: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, China

No 2019, Working Papers from Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon

Abstract: Two new notions of stability of coalitions, based on the idea of exclusion or integration of players depending on how they affect allocations, are introduced for cooperative transferable utility games. The first one, called internal stability, requires that no coalition member would find that her departure from the coalition would improve her allocation or those of all her partners. The second one, called external stability, requires that coalitions members do not wish to recruit a new partner willing to join the coalition, since her arrival would hurt some of them. As an application of these two notions, we study the stability of Group Purchasing Organizations using the Shapley value to allocate costs between buyers. Our main results suggest that, when all buyers are initially alone, while small buyers will form internally and externally stable Group Purchasing Organizations to benefit from the best price discount, big buyers will be mutually exclusive and may cooperate with only small buyers.

Keywords: Internal and external stability; Group purchasing organization; Cost allocation; Shapley value (search for similar items in EconPapers)
JEL-codes: C71 D61 D62 (search for similar items in EconPapers)
Date: 2020
New Economics Papers: this item is included in nep-cdm, nep-des, nep-gth and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Working Paper: On the Internal and External Stability of Coalitions and Application to Group Purchasing Organizations (2020)
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