Analysis of the impact of DMUs on the overall efficiency in the event of a merger

This paper addresses several mechanisms for overall ranking Decision Making Units (DMUs) according to the contribution of DMUs to the relative efficiency score of a merger considering aggregate units The possible organization of agents outside each possible merger naturally influences the relative efficiency score, which motivates the use of games in partition function form and specific ranking indices for DMUs based on the Shapley value. Several computational problems arise in their exact computation when the number of DMUs increases. We describe two sampling alternatives to reduce these drawbacks. Finally, we apply these methods to analyse the efficiency of the hotel industry in SpainThis work has been supported by FEDER/Ministerio de Ciencia, Innovación y Universidades - Agencia Estatal de Investigación, Spain under grants MTM2017-87197-C3-2-P and MTM2017-87197-C3-3-P, and by the Xunta de Galicia through the European Regional Development Fund (Grupos de Referencia Competitiva ED431C-2017/38) and by the Consellería de Cultura, Educación e Universidades, Xunta de Galicia, Spain (Grupos de Referencia Competitiva ED431C-2020/03).S

A Focal-Point Solution for Bargaining Problems with Coalition Structure

In this paper we study the restriction, to the class of bargaining problems with coalition structure, of several values which have been proposed on the class of non-transferable utility games with coalition structure. We prove that all of them coincide with the solution independently studied in Chae and Heidhues (2004) and Vidal-Puga (2005a). Several axiomatic characterizations and two noncooperative mechanisms are proposed.coalition structure bargaining values

Power Indices and Minimal Winning Coalitions in Simple Games with Externalities

We propose a generalization of simple games to sit uations with coalitional externalities. The main novelty of our generalization is a monotonicity property that we define for games in partition function form. This property allows us to properly speak about minimal winning embedded coalitions. We propose and characterize two power indices based on these kind of coalitions. We provide methods based on the multilinear extension of the game to compute the indices. Finally, the new indices are used to study the distribution of power in the current Parliament of Andalusia

The Least Square Nucleolus is a Normalized Banzhaf Value

In this note we study a truncated additive normalization of the Banzhaf value. We are able to show that it corresponds to the Least Square nucleolus (LS-nucleolus), which was originally introduced as the solution of a constrained optimization problem (Ruiz et al., 1996). Thus, the main result provides an explicit expression that eases the computation and contributes to the understanding of the LS-nucleolus. Lastly, the result is extended to the broader family of Individually Rational Least Square values (Ruiz et al., 1998b)

Power indices and minimal winning coalitions for simple games in partition function form

We propose a generalization of simple games to partition function form games based on a monotonicity property that we define in this context. This property allows us to properly speak about minimal winning embedded coalitions. We propose and characterize two power indices based on such coalitions. Finally, the new indices are used to study the distribution of power in the Parliament of Andalusia that emerged after the elections of March 22, 2015

On the externality free shapley-shubik index

We address the problem of extending the Shapley-Shubik index to the class of simple games with externalities introduced in Alonso-Meijide et al. (2017). On the one hand, we provide bounds for any efficient, symmetric, and monotonic power index. On the other hand, we characterize the restriction of the externality-free value of de Clippel and Serrano (2008) to the class of games under study by adapting well-known properties

The Shapley-Shubik Index in the Presence of Externalities

In this note we characterize the restriction of the externality-free value of de Clippel and Serrano (2008) to the class of simple games with externalities introduced in Alonso-Meijide et al. (2015

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

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

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