On egalitarian values for cooperative games with a priori unions
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On egalitarian values for cooperative games with a priori unions J. M. Alonso‑Meijide1 · J. Costa2 · I. García‑Jurado3 · J. C. Gonçalves‑Dosantos3 Received: 18 October 2019 / Accepted: 14 March 2020 © Sociedad de Estadística e Investigación Operativa 2020
Abstract In this paper, we extend the equal division and the equal surplus division values for transferable utility cooperative games to the more general setup of transferable utility cooperative games with a priori unions. In the case of the equal surplus division value we propose three possible extensions. We provide axiomatic characterizations of the new values. Furthermore, we apply the proposed modifications to a particular motivating example and compare the numerical results with those obtained with the original values. Keywords Cooperative games · A priori unions · Equal division value · Equal surplus division value Mathematics Subject Classification 91A12 · 91A80
This work has been supported by the ERDF, the MINECO/AEI grants MTM2017-87197-C31-P, MTM2017-87197-C3-3-P, and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2016-015 and ED431C-2017/38 and Centro Singular de Investigación de Galicia ED431G/01). The authors would like to thank two anonymous referees for their helpful suggestions to improve this article. * I. García‑Jurado [email protected] 1
Grupo MODESTYA, Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, Facultade de Ciencias, Campus de Lugo, 27002 Lugo, Spain
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Grupo MODES, Departamento de Matemáticas, Universidade da Coruña, Campus de Elviña, 15071 A Coruña, Spain
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Grupo MODES, CITIC and Departamento de Matemáticas, Universidade da Coruña, Campus de Elviña, 15071 A Coruña, Spain
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1 Introduction Many economic problems deal with situations in which several agents cooperate to generate benefits or to reduce costs. Cooperative game theory studies procedures to allocate the resulting benefits (or costs) among the cooperating agents in those situations. One of the most commonly used allocating procedures is the Shapley value, introduced in Shapley (1953) and analyzed more recently in Moretti and Patrone (2008) or in Algaba et al. (2019). Very often, however, agents cooperate on the basis of a kind of egalitarian principle according to which the benefits will be shared equitably. For instance, Selten (1972) indicates that egalitarian considerations explain in a successful way observed outcomes in experimental cooperative games. In recent years, the game theoretical literature has dealt with several egalitarian solutions in cooperative games. For instance, van den Brink (2007) provides a comparison of the equal division value and the Shapley value, and Casajus and Hüttner (2014) compare those two solutions with the equal surplus division value (studied first in Driessen and Funaki 1991). In van den Brink and Funaki (2009), Chun and Park (2012), van den Brink et al. (2016), Ferrières (2017) and Béal et al. (2
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