On the centrality analysis of covert networks using games with externalities

The identification of the most potentially hazardous agents in a terrorist organisation helps to prevent further attacks by effectively allocating surveillance resources and destabilising the covert network to which they belong. In this paper, several mechanisms for the overall ranking of covert networks members in a general framework are addressed based on their contribution to the overall relative effectiveness in the event of a merger. In addition, the possible organisation of agents outside of each possible merger naturally influences their relative effectiveness score, which motivates the innovative use of games in partition function form and specific ranking indices for individuals. Finally, we apply these methods to analyse the effectiveness of the hijackers of the covert network supporting the 9/11 attacksThis work is part of the R+D+I project grants MTM2017-87197-C3-3-P and PID2021-124030NB-C32, funded byMCIN/AEI/10.13039/501100011033/ and by “ERDF A way of making Europe”/EU. This research was also funded by Grupos de Referencia Competitiva ED431C-2021/24 from the Consellería de Cultura, Educación e Universidades, Xunta de Galicia.S

Generating functions: a useful tool for computing power indices

In the theory of simple games, the study of power indices plays an important role. One of the main di culties with these indices is that computation generally requires the sum of a very large number of terms. The generating functions are e cient tools to make more easy this computation. In this paper, we provide a revision of the main elements of this method when we use it to compute the Shapley-Shubik and the BanzhafColeman power indices. Further, we provide a new method to compute the Banzhaf-Coleman indexS

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

Assessment of the influence of features on a classification problem: an application to COVID-19 patients

This paper deals with an important subject in classification problems addressed by machine learning techniques: the evaluation of the influence of each of the features on the classification of individuals. Specifically, a measure of that influence is introduced using the Shapley value of cooperative games. In addition, an axiomatic characterisation of the proposed measure is provided based on properties of efficiency and balanced contributions. Furthermore, some experiments have been designed in order to validate the appropriate performance of such measure. Finally, the methodology introduced is applied to a sample of COVID-19 patients to study the influence of certain demographic or risk factors on various events of interest related to the evolution of the diseaseThe authors are grateful to Ricardo Cao Abad and to the Dirección Xeral de Saúde Pública of the Xunta de Galicia in Spain. This work has been supported by the ERDF, the Government of Spain/AEI [grants MTM2017-87197-C3-1-P and MTM2017-87197-C3-3-P]; the Xunta de Galicia [Grupos de Referencia Competitiva ED431C2016-015, ED431C2017/38, and ED431C 2021/24, and Centro Singular de Investigación de Galicia ED431G/01]; and by the collaborative research project of the IMAT “Mathematical, statistical and dynamic study of the epidemic COVID-19”, subsidized by the Vice-Rector’s Office for Research and Innovation at the University of Santiago de Compostela, Spain. The research of Laura Davila-Pena has been funded by the Government of Spain [grant FPU17/02126]. We would also like to thank the three anonymous referees and the editor for their constructive comments and suggestions, which helped us to improve the final version of this paperS

Assessment of the Influence of Features on a Classification Problem: An Application to COVID-19 Patients

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[Abstract] This paper deals with an important subject in classification problems addressed by machine learning techniques: the evaluation of the influence of each of the features on the classification of individuals. Specifically, a measure of that influence is introduced using the Shapley value of cooperative games. In addition, an axiomatic characterisation of the proposed measure is provided based on properties of efficiency and balanced contributions. Furthermore, some experiments have been designed in order to validate the appropriate performance of such measure. Finally, the methodology introduced is applied to a sample of COVID-19 patients to study the influence of certain demographic or risk factors on various events of interest related to the evolution of the disease.The authors are grateful to Ricardo Cao Abad and to the Dirección Xeral de Saúde Pública of the Xunta de Galicia in Spain. This work has been supported by the ERDF, the Government of Spain/AEI [grants MTM2017-87197-C3-1-P and MTM2017-87197-C3-3-P]; the Xunta de Galicia [Grupos de Referencia Competitiva ED431C2016-015, ED431C2017/38, and ED431C 2021/24, and Centro Singular de Investigación de Galicia ED431G/01]; and by the collaborative research project of the IMAT “Mathematical, statistical and dynamic study of the epidemic COVID-19”, subsidized by the Vice-Rector’s Office for Research and Innovation at the University of Santiago de Compostela, Spain. The research of Laura Davila-Pena has been funded by the Government of Spain [grant FPU17/02126]Xunta de Galicia; ED431C2016-015Xunta de Galicia; ED431C2017/38Xunta de Galicia; ED431C 2021/24Xunta de Galicia; ED431G/0

An Integer Linear Programming Model to Select and Temporally Allocate Resources for Fighting Forest Fires

Optimal planning of the amount and type of resources needed for extinguishing a forest fire is a task that has been addressed in the literature, using models obtained from operational research. In this study, a general integer linear programming model is proposed, which addresses the allocation of resources in different time periods during the planning period for extinguishing a fire, and with the goal of meeting Spanish regulations for the non-negligence of fronts and periods of rest for pilots and brigades. A computer program and interface were developed using the R language. By means of an example using historical data, we illustrate the model at work and its exact resolution. Then, we carry out a simulation study to analyze the obtained objective functions and resolution times. Our simulation study shows that an exact solution can be obtained very quickly without requiring heuristic algorithms, provided that the planning period does not exceed five hoursThis research received financial support from Ministerio de Economía y Competitividad of Spain through grants MTM2014-53395-C3-2-P, MTM2016-76969-P and MTM2017-87197-C3-3-P, and from ITMATI, Technological Institute of Industrial Mathematics, Santiago de Compostela, Spain, through the Enjambre project. Both are gratefully acknowledgedS

Cost allocation problems on highways with grouped users

One of the practical applications of cooperative transferable utility games involves determining the fee structure for users of a given facility, whose construction or maintenance costs need to be recouped. In this context, certain efficiency and equity criteria guide the considered solutions. This paper analyzes how to allocate the fixed costs of a highway among its users through tolls, considering that different classes of vehicles or travelers utilize the service. For this purpose, we make use of generalized highway games with a priori unions that represent distinct user groups, such as frequent travelers or truckers, who, due to enhanced bargaining power, often secure reductions in their fares in real-world scenarios. In particular, the Owen value, the coalitional Tijs value, and a new value termed the Shapley-Tijs value are axiomatically characterized. Additionally, straightforward formulations for calculating these values are provided. Finally, the proposed methodology is applied to actual traffic data from the AP-9 highway in Spain

Allocation Rules for Games with Optimistic Aspirations

A game with optimistic aspirations specifies two values for each coalition of players: the first value is the worth that the players in the coalition can guarantee for themselves in the event that they coordinate their actions, and the second value is the amount that the players in the coalition aspire to get under reasonable but very optimistic assumptions about the demands of the players who are not included in the coalition. In this paper, in addition to presenting this model and justifying its relevance, we introduce allocation rules and extend the properties of efficiency, additivity, symmetry, and null player property to this setting. We demonstrate that these four properties are insufficient to find a unique allocation rule and define three properties involving null players and nullifying players that allow the identification of unique allocation rules. The allocation rules we identify are the Midpoint Shapley Value and the Equal Division RuleThey also acknowledge the financial support of the University of Santiago de Compostela, of Ministerio de Ciencia e Innovación through Projects ECO2008-03484-C02-02 and MTM2011-27731-C03, and of Xunta de Galicia through Project INCITE09-207-064-PRS