arXiv subjects

J. C. Gonçalves-Dosantos

Publications and source records attributed to J. C. Gonçalves-Dosantos.

7 recordsLinked to original sources

arXiv2026

Null player neutrality in TU-games: Egalitarian and Shapley solutions

We introduce and study the axiom of null player neutrality in the context of cooperative games with transferable utility (TU-games). This axiom weakens the classical coalitional strategic equivalence: rather than requiring that augmenting a game by a null-player game leaves that player's payoff unchanged, it only requires that any change in payoff be independent of the specific augmenting game, provided both the null-player condition and the grand-coalition value are preserved. We show that efficiency, linearity, symmetry, and null player neutrality together characterize the family of all real linear combinations of the Shapley value and the equal division solution, a family that strictly extends the well-known class of $α$-egalitarian Shapley values (convex combinations, $α\in [0,1]$) to arbitrary $α\in \mathbb{R}$. Replacing null player neutrality by its natural analogue for nullifying players uniquely pins down the equal division solution.

econ.TH↗

arXiv2025

Cost allocations in interval inventory situations: the SOC and Shapley approaches

Uncertainty in demand and supply conditions poses critical challenges to effective inventory management, especially in collaborative environments. Traditional inventory models, such as those based on the Economic Order Quantity (EOQ), often rely on fixed parameters and deterministic assumptions, limiting their ability to capture the complexity of real-world scenarios. This paper focuses on interval inventory situations, an extension of classical models in which demand is represented as intervals to account for uncertainty. This framework allows for a more flexible and realistic analysis of inventory decisions and cost-sharing among cooperating agents. We examine two interval-based allocation rules, the interval SOC-rule and the interval Shapley rule, designed to distribute joint ordering costs fairly and efficiently under uncertain demand. Their theoretical properties are analyzed, and their practical applicability is demonstrated through a case study involving the coordination of perfume inventories across seven Spanish airports, based on 2023 passenger traffic data provided by AENA. The findings highlight the potential of interval-based models to enable a robust and equitable allocation of inventory costs in the face of operational uncertainty.

math.OC↗

arXiv2024

On egalitarian values for cooperative games with level structures

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 level structures. In the case of the equal surplus division value we propose three possible extensions, one of which has already been described in the literature. We provide axiomatic characterizations of the values considered, apply them to a particular cost sharing problem and compare them in the framework of such an application.

cs.GT↗

arXiv2024

Sharing delay costs in stochastic scheduling problems with delays

An important problem in project management is determining ways to distribute amongst activities the costs that are incurred when a project is delayed because some activities end later than expected. In this study, we address this problem in stochastic projects, where the durations of activities are unknown but their corresponding probability distributions are known. We propose and characterise an allocation rule based on the Shapley value, illustrate its behaviour by using examples, and analyse features of its calculation for large problems.

cs.GT↗

arXiv2024

Necessary players and values

In this paper we introduce the $Γ$ value, a new value for cooperative games with transferable utility. We also provide an axiomatic characterization of the $Γ$ value based on a property concerning the so-called necessary players. A necessary players of a game is one without which the characteristic function is zero. We illustrate the performance of the $Γ$ value in a particular cost allocation problem that arises when the owners of the apartments in a building plan to install an elevator and share its installation cost; in the resulting example we compare the proposals of the $Γ$ value, the equal division value and the Shapley value in two different scenarios. In addition, we propose an extension of the $Γ$ value for cooperative games with transferable utility and with a coalition structure. Finally, we provide axiomatic characterizations of the coalitional $Γ$ value and of the Owen and Banzhaf-Owen values using alternative properties concerning necessary players.

cs.GT↗

arXiv2024

On egalitarian values for cooperative games with a priori unions

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 cost sharing problem and compare the numerical results with those obtained with the original values.

cs.GT↗

arXiv2024

New results on egalitarian values for games with a priori unions

Several extensions of the equal division value and the equal surplus division value to the family of games with a priori unions are proposed in Alonso-Meijide et al. (2020) ``On egalitarian values for cooperative games with a priori unions.'' TOP 28: 672-688. In this paper we provide new axiomatic characterizations of these values. Furthermore, using the equal surplus division value in two steps, we propose a new coalitional value. The balanced contributions and quotient game properties give rise to a different modification of the equal surplus division value.

cs.GT↗