Mergeable weighted majority games and characterizations of some power indices

In this paper, we introduce a notion of mergeable weighted majority games with the aim of providing the first characterization of the Colomer–Martínez power index (Colomer and Martínez in J Theor Polit 7(1):41–63, 1995). Furthermore, we define and characterize a new power index for the family of weighted majority games that combines ideas of the Public Good (Holler in Polit Stud 30(2):262–271, 1982) and Colomer–Martínez power indices. Finally, we analyze the National Assembly of Ecuador using these and some other well-known power indicesWe would like to thank Balbina V. Casas-Méndez and two anonymous referees for their valuable comments. This work is part of the R+D+I project grants MTM2017-87197-C3-2-P, MTM2017-87197-C3-3-P, PID2021-124030NB-C32, and PID2021-124030NB-C33, that were funded by MCIN/AEI/10.13039/501100011033/ and by “ERDF A way of making Europe”/EU. This research was also funded by Grupos de Referencia Competitiva ED431C-2020/03 and ED431C-2021/24 from the Consellería de Cultura, Educación e Universidades, Xunta de Galicia. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer NatureS

On horizontal cooperation in linear production processes with a supplier that controls a limited resource

In this paper we consider a two-echelon supply chain with one supplier that controls a limited resource and a finite set of manufacturers who need to purchase this resource. We analyze the effect of the limited resource on the horizontal cooperation of manufacturers. To this end, we use cooperative game theory and the existence of stable distributions of the total profit among the manufacturers as a measure of the possibilities of cooperation. The game theoretical model that describes the horizontal cooperation involves externalities, which arise because of the possible scarcity of the limited resource and the possible coalition structures that can be formed. Furthermore, manufacturers do not know how the supplier will allocate the limited resource, therefore, how much of this resource they will obtain is uncertain for all concerned. Nevertheless, when the limited resource is not scarce for the grand coalition, the existence of stable distributions of the total profit is guaranteed and consequently the collaboration among the manufacturers is profitable for them all. In the event that the limited resource is insufficient for the grand coalition, we introduce a new cooperative game that assesses the expectations of each coalition of manufacturers regarding the amount of the limited resource they can obtain. We analyze two extreme expectations: the optimistic and the pessimistic. In the optimistic case, we cannot reach a conclusion regarding the full cooperation of the manufacturers. In the pessimistic case, with one reasonable assumption, the existence of stable distributions of the total profit is guaranteed and as a result the collaboration among manufacturers is a win–win deal.Ministerio de Economía y Competitividad | Ref. MTM2014-54199-PMinisterio de Economía y Competitividad | Ref. MTM2014-53395-C3-3-PFundación Séneca | Ref. 19320/PI/1

Cooperative Games and Coalition Cohesion Indices: The Choquet–Owen Value

In a cooperative game with transferable utility, it is usually assumed that all coalitions are equally feasible. However, if we deal with cooperative games with coalition configuration, only some coalitions are a priori feasible, due to the preferences of the agents. In this paper, we propose a generalization of games with coalition configuration. In our model, the feasibility of a coalition is determined by the cohesion of its members, and obviously, this cohesion does not have to be equal for all coalitions. The cohesion of each coalition will be determined by a cohesion index. We introduce the class of games with cohesion index and propose an allocation rule, which is characterized by using reasonable properties. The cohesion idea is not only a concept related to social groups. In software design, this concept explains the relationships among all the elements of a module. Our value can be applied in this way as we show in the paper

A Bankruptcy Approach to the Core Cover

In this paper we establish a relationship between the core cover of a compromise admissiblegame and the core of a particular bankruptcy game: the core cover of a compromiseadmissible game is, indeed, a translation of the set of coalitional stable allocations capturedby an associated bankruptcy game. Moreover, we analyze the combinatorial complexity ofthe core cover and, consequently, of the core of a compromise stable game

A sampling approach for the approximation of the Deegan-Packel index

In this paper, we address a sampling procedure for approximating the Deegan-Packel index, which is particularly advantageous when tackling with large-scale problems. It is based on the estimation of an expectation in a subdomain. Its performance is analyzed in terms of statistical properties and of bounds for the incurred absolute error. The effectiveness of this tool is demonstrated through a real-world example where this power index can be exactly computed. Finally, we use it to determine a new power distribution for two compositions of the Board of Governors of the International Monetary Fund (IMF). The resulting distributions of the power are compared with the ones prescribed by the Shapley and the Banzhaf values.Xunta de Galicia | Ref. ED431C-2020/03Xunta de Galicia | Ref. ED431C-2021/24Agencia Estatal de Investigación | Ref. PID2021-124030NB-C33Agencia Estatal de Investigación | Ref. PID2021-124030NB-C3

Evaluating the impact of items and cooperation in inventory models with exemptable ordering costs

In this paper we introduce and analyse, from a game theoretical perspective, several multi-agent or multi-item continuous review inventory models in which the buyers are exempted from ordering costs if the price of their orders is greater than or equal to a certain amount. For all models we obtain the optimal ordering policy. We first analyse a simple model with one firm and one item. Then, we study a model with one firm and several items, for which we design a procedure based on cooperative game theory to evaluate the impact of each item on the total cost. Then, we deal with a model with several firms and one item for each firm, for which we characterise a rule to allocate the total cost among the firms in a coalitionally stable way. Finally, we discuss a model with several firms and several items, for which we characterise a rule to allocate the total cost among the firms in a coalitionally stable way and to evaluate the impact of each item on the cost that would be payable to each firm when using the allocation rule. All the concepts and results of this article are illustrated using data from a case study.Agencia Estatal de Investigación | Ref. MTM2017-87197-C3-1-PAgencia Estatal de Investigación | Ref. MTM2017-87197-C3-2-PAgencia Estatal de Investigación | Ref. PGC2018-097965-B-I00Agencia Estatal de Investigación | Ref. PID2021-124030NB-C31Agencia Estatal de Investigación | Ref. PID2021-124030NB-C33MCIN/AEI/10.13039/501100011033/ | Ref. PID2022-137211NB-100Comunidad Valenciana | Ref. PROMETEO/2021/063Xunta de Galicia | Ref. ED431C-2020/03Xunta de Galicia | Ref. ED431C-2020/14Universidade da Coruña/CISU

Cooperation on capacitated inventory situations with fixed holding costs

[Abstract] In this paper we analyze a situation in which several firms deal with inventory problems concerning the same type of product. We consider that each firm uses its limited capacity warehouse for storing purposes and that it faces an economic order quantity model where storage costs are irrelevant (and assumed to be zero) and shortages are allowed. In this setting, we show that firms can save costs by placing joint orders and obtain an optimal order policy for the firms. Besides, we identify an associated class of costs games which we show to be concave. Finally, we introduce and study a rule to share the costs among the firms which provides core allocations and can be easily computed.Ministerio de Ciencia e Innovación; MTM2011-23205Galicia. Consellería de Economía e Industria; INCITE09-207-064-PRComunidad Valenciana. Generalidad; ACOMP/2014Ministerio de Ciencia e Innovación; MTM2011-27731-C0

On benefits of cooperation under strategic power

We introduce a new model involving TU-games and exogenous structures. Specifically, we consider that each player in a population can choose an element in a strategy set and that, for every possible strategy profile, a TU-game is associated with the population. This is what we call a TU-game with strategies. We propose and characterize the maxmin procedure to map every game with strategies to a TU-game. We also study whether or not the relevant properties of TU-games are transmitted by applying the maxmin procedure. Finally, we examine two relevant classes of TU-games with strategies: airport and simple games with strategies.Ministerio de Economía y Competitividad | Ref. PGC2018-097965-B-100Ministerio de Economía y Competitividad | Ref. MTM2017-87197-C3-1-PMinisterio de Economía y Competitividad | Ref. MTM2017-87197-C3-2-PMinisterio de Economía y Competitividad | Ref. MTM2014-53395-C3-1-PMinisterio de Economía y Competitividad | Ref. MTM2014-53395-C3-3-PMinisterio de Economía y Competitividad | Ref. MTM2014-54199-PXunta de Galicia | Ref. ED431C-2016-015Xunta de Galicia | Ref. ED431C-2016-040Xunta de Galicia | Ref. ED431G/0

Evaluating the impact of items and cooperation in inventory models with exemptable ordering costs

[Absctract]: In this paper we introduce and analyse, from a game theoretical perspective, several multi-agent or multi-item continuous review inventory models in which the buyers are exempted from ordering costs if the price of their orders is greater than or equal to a certain amount. For all models we obtain the optimal ordering policy. We first analyse a simple model with one firm and one item. Then, we study a model with one firm and several items, for which we design a procedure based on cooperative game theory to evaluate the impact of each item on the total cost. Then, we deal with a model with several firms and one item for each firm, for which we characterise a rule to allocate the total cost among the firms in a coalitionally stable way. Finally, we discuss a model with several firms and several items, for which we characterise a rule to allocate the total cost among the firms in a coalitionally stable way and to evaluate the impact of each item on the cost that would be payable to each firm when using the allocation rule. All the concepts and results of this article are illustrated using data from a case study.This work is part of the R+D+I project grants MTM2017-87197-C3-1-P, MTM2017-87197-C3-2-P, PGC2018-097965-B-I00, PID2021-124030NB-C31, PID2021-124030NB-C33 and PID2022-137211NB-100, that were funded by MCIN/AEI/10.13039/501100011033/ and by “ERDF A way of making Europe”/EU. This research was also funded by project PROMETEO/2021/063 from the Comunidad Valenciana, and by Grupos de Referencia Competitiva ED431C-2020/03 and ED431C-2020/14 from the Consellería de Cultura, Educación e Universidades, Xunta de Galicia. Funding for open access charge: Universidade da Coruña/CISUG . The authors would also like to thank the anonymous reviewers for their comments, which have contributed to the improvement of this article.Xunta de Galicia; ED431C-2020/03Xunta de Galicia; ED431C-2020/14Generalitat Valenciana; PROMETEO/2021/06

On benefits of cooperation under strategic power

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https:// doi.org/10.1007/s10479-019-03495-6[Abstract]: We introduce a new model involving TU-games and exogenous structures. Specifically, we consider that each player in a population can choose an element in a strategy set and that, for every possible strategy profile, a TU-game is associated with the population. This is what we call a TU-game with strategies. We propose and characterize the maxmin procedure to map every game with strategies to a TU-game. We also study whether or not the relevant properties of TU-games are transmitted by applying the maxmin procedure. Finally, we examine two relevant classes of TU-games with strategies: airport and simple games with strategies.The authors would like to thank two anonymous referees for their helpful suggestions to improve this article. This work has been supported by the Ministerio de Economía y Competitividad through Grants PGC2018-097965-B-100, MTM2017-87197-C3-1-P, MTM2017-87197-C3-2-P, MTM2014-53395-C3-1-P, MTM2014-53395-C3-3-P, MTM2014-54199-P, and by the Xunta de Galicia through the European Regional Development Fund (Grupos de Referencia Competitiva ED431C-2016-015 and ED431C-2016-040, and Centro Singular de Investigación de Galicia ED431G/01).Xunta de Galicia; ED431C-2016-015Xunta de Galicia; ED431C-2016-040Xunta de Galicia; ED431G/0