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

Computing Banzhaf–Coleman and Shapley–Shubik power indices with incompatible players

In this paper, we present methods to compute Banzhaf–Coleman and Shapley–Shubik power indices for weighted majority games when some players are incompatible. We use the so-called generating functions as a tool.Ministerio de Ciencia e Innovación | Ref. MTM2011-27731-C0

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 [4]. 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 [6].Ministerio de Ciencia e Innovación | Ref. MTM2011-27731-C02Ministerio de Ciencia e Innovación | Ref. MTM2011-27731-C0

Sequencing situations and games with non-linear cost functions under optimal order consistency

This paper considers sequencing situations with non-linear cost functions under optimal order consistency. Specifically, we study sequencing situations with discounting cost functions and logarithmic cost functions of the completion time. In both settings, we show that the neighbor switching gains are non-negative and non-decreasing for every misplaced pair of players. We derive new conditions on the time-dependent neighbor switching gains in a sequencing situation under optimal order consistency to guarantee convexity of the associated sequencing game. Furthermore, we define two types of gain splitting rules for the class of sequencing situations under optimal order consistency. Each one of them is based on a procedure that specifies a path from the initial order to an optimal order, dividing the neighbor switching gains in every step among the two involved players. We prove that these allocations are stable under the same conditions that are required for convexity. These requirements are fulfilled for discounting and logarithmic sequencing situations, as well as in other settings, such as in sequencing situations with exponential cost functions.Ministerio de Ciencia, Innovación y Universidades | Ref. MTM2017-87197-C3-2-PMinisterio de Ciencia, Innovación y Universidades | Ref. MTM2017-87197- C3-3-PXunta de Galicia | Ref. ED431C- 2016-040Xunta de Galicia | Ref. ED431C-2017/38Xunta de Galicia | Ref. ED431C2020-0

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., 201

"k"-core covers and the core

This paper extends the notion of individual minimal rights for a transferable utility game (TU-game) to coalitional minimal rights using minimal balanced families of a specific type, thus defining a corresponding minimal rights game. It is shown that the core of a TU-game coincides with the core of the corresponding minimal rights game. Moreover, the paper introduces the notion of the k-core cover as an extension of the core cover. The k-core cover of a TU-game consists of all efficient payoff vectors for which the total joint payoff for any coalition of size at most k is bounded from above by the value of this coalition in the corresponding dual game, and from below by the value of this coalition in the corresponding minimal rights game. It is shown that the core of a TU-game with player set N coincides with the b jNj 2 c-core cover. Furthermore, full characterizations of games for which a k-core cover is nonempty and for which a k-core cover coincides with the core are provided.Ministerio de Ciencia e Innovación | Ref. MTM2011-27731-C0

On the 1-nucleolus

This paper analyzes the 1-nucleolus and, in particular, its relation to the nucleolus. It is seen that, contrary to the nucleolus, the 1-nucleolus can be computed in polynomial time due to a characterization using a combination of standard bankruptcy rules for associated bankruptcy problems. Sufficient conditions on a compromise stable game are derived such that the 1-nucleolus and the nucleolus coincide.Ministerio de Ciencia e Innovación | Ref. MTM2011-27731-C03Ministerio de Economía y Competitividad | Ref. MTM2014-53395-C3-3-

Marginality and convexity in partition function form games

In this paper an order on the set of embedded coalitions is studied in detail. This allows us to define new notions of superaddivity and convexity of games in partition function form which are compared to other proposals in the literature. The main results are two characterizations of convexity. The first one uses non-decreasing contributions to coalitions of increasing size and can thus be considered parallel to the classic result for cooperative games without externalities. The second one is based on the standard convexity of associated games without externalities that we define using a partition of the player set. Using the later result, we can conclude that some of the generalizations of the Shapley value to games in partition function form lie within the cores of specific classic games when the original game is convexThis work has been supported by FEDER/Ministerio de Ciencia, Innovación y Universidades – Agencia Estatal de Investigación/MTM2017-87197-C3-2-P, /MTM2017-87197-C3-3-P,/ PID2020-113110GB-L00, /MTM2017-83455-P, by the Generalitat de Catalonia through grant 2017-SGR-778, by the Junta de Andalucía through grant FQM237, and by the Xunta de Galicia through the European Regional Development Fund (Grupos de Referencia Competitiva ED431C-2016-040 and ED431C-2017/38)S