Evaluation de la valeur de Shapley et son application au calcul du pouvoir des provinces canadiennes dans le vote d'un projet de loi au parlement.

Rapport de recherche

Production externalities : cooperative and non-cooperative approaches

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

A Shapley value analysis to coordinate the formation of procurement

In this paper we address the problem of forming procurement networks for items with value adding stages that are linearly arranged. Formation of such procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions. Recent research in supply chain management has emphasized that such decisions need to take into account the fact that suppliers and buyers are intelligent and rational agents who act strategically. In this paper, we view the problem of Procurement Network Formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a fair manner. We study the implications of using the Shapley value as a solution concept for forming such procurement networks. We also present a protocol, based on the extensive form game realization of the Shapley value, for forming these networks.

The core and shapley value analysis for cooperative formation of procurement networks

Formation of high value procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions, where suppliers are intelligent and rational agents who act strategically. In this paper we address the problem of forming procurement networks for items with value adding stages that are linearly arranged We model the problem of Procurement Network Formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a stable and fair manner We first investigate the stability of such networks by examining the conditions under which the core of the game is non-empty. We then present a protocol, based on the extensive form game realization of the core, for forming such networks so that the resulting network is stable. We also mention a key result when the Shapley value is applied as a solution concept.

Participes présents et gérondifs en traduction finnoise : perte ou changement de valeur ?

Les participes présents apparaissent, entre autres, dans des constructions à prédication seconde détachées : (1) Intervenant hier soir à Ankara, […], Vladimir Poutine s’est risqué à […]. (Le Figaro 7.12.2004 : 4) Même si les gérondifs, formes adverbiales du verbe (« converbes », cf. Haspelmath & König 1995), n’ont pas d’incidence nominale, contrairement aux participes présents, formes adjectivales du verbe, et ne sont donc pas toujours comptés parmi les constructions à prédication seconde (p.ex. Neveu 1998), les deux ont des emplois assez proches : dans des énoncés du type (2a-b), le participe adjoint peut être paraphrasé par un gérondif, même si son statut fonctionnel n’est pas le même (Halmøy, 2003 : 156-157) : (2a) Arrivant à Paris, Emile a proposé à Léa de [...]. (2b) En arrivant à Paris, Emile a proposé à Léa de[...]. (Halmøy, 2003 : 157) Le finnois ne connaît ni ce genre de constructions détachés ni de forme appelée ‘gérondif’, et les deux participes présents finnois (actif et passif) ne correspondent jamais à un participe présent détaché français : en plus de subordonnées, on trouve à leur place le deuxième infinitif, soit à l’inessif, soit à l’instructif, formes nominales qu’on trouve également dans la traduction des gérondifs : (3a) […] ? me demanda-t-elle sèchement en me montrant l’une des lignes incriminées. (Nothomb, p. 62) […] : hän kysyi minulta kuivakkaasti näyttäen erästä Unajin moittimaa riviä. (Suni, p. 4) (3b) L’espace d’un instant, il sourit, croyant que […] je m’étais trompée de commodités. (Nothomb, p. 138-139) Hetken hän hymyili luullen, että minä […] olin erehtynyt mukavuuslaitoksesta. (Suni, p. 94) : Dans cette communication, nous examinerons quatre traductions littéraires en nous demandant dans quels cas et de quelle manière la différence entre le participe et le gérondif a éventuellement été prise en considération.

Cohésion modale et subordination : Le conditionnel et le jussif finnois au miroir de la valeur sémantique et discursive du subjonctif français

Modal cohesion and subordination. The Finnish conditional and jussive moods in comparison to the French subjunctive This study examines verb moods in subordinate clauses in French and Finnish. The first part of the analysis deals with the syntax and semantics of the French subjunctive, mood occurring mostly in subordinate positions. The second part investigates Finnish verb moods. Although subordinate positions in Finnish grammar have no special finite verb form, certain uses of Finnish verb moods have been compared to those of subjunctives and conjunctives in other languages. The present study focuses on the subordinate uses of the Finnish conditional and jussive (i.e. the third person singular and plural of the imperative mood). The third part of the analysis discusses the functions of subordinate moods in contexts beyond complex sentences. The data used for the analysis include 1834 complex sentences gathered from newspapers, online discussion groups and blog texts, as well as audio-recorded interviews and conversations. The data thus consist of both written and oral texts as well as standard and non-standard variants. The analysis shows that the French subjunctive codes theoretical modality. The subjunctive does not determine the temporal and modal meaning of the event, but displays the event as virtual. In a complex sentence, the main clause determines the temporal and modal space within which the event coded by the subjunctive clause is interpreted. The subjunctive explicitly indicates that the space constructed in the main clause extends its scope over the subordinate clause. The subjunctive can therefore serve as a means for creating modal cohesion in the discourse. The Finnish conditional shares the function of making explicit the modal link between the components of a complex construction with the French subjunctive, but the two moods differ in their semantics. The conditional codes future time and can therefore occur only in non-factual or counterfactual contexts, whereas the event expressed by French subjunctive clauses can also be interpreted as realized. Such is the case when, for instance, generic and habitual meaning is involved. The Finnish jussive mood is used in a relatively limited number of subordinate clause types, but in these contexts its modal meaning is strikingly close to that of the French subjunctive. The permissive meaning, typical of the jussive in main clause positions, is modified in complex sentences so that it entails inter-clausal relation, namely concession. Like the French subjunctive, the jussive codes theoretical modal meaning with no implication of the truth value of the proposition. Finally, the analysis shows that verb moods mark modal cohesion, not only on the syntagmatic level (namely in complexe sentences), but also on the paradigmatic axis of discourse in order to create semantic links over entire segments of talk. In this study, the subjunctive thus appears, not as an empty category without function, as it is sometimes described, but as an open form that conveys the temporal and modal meanings emerging from the context.

A Shapley Value-Based Approach to Discover Influential Nodes in Social Networks

Our study concerns an important current problem, that of diffusion of information in social networks. This problem has received significant attention from the Internet research community in the recent times, driven by many potential applications such as viral marketing and sales promotions. In this paper, we focus on the target set selection problem, which involves discovering a small subset of influential players in a given social network, to perform a certain task of information diffusion. The target set selection problem manifests in two forms: 1) top-k nodes problem and 2) lambda-coverage problem. In the top-k nodes problem, we are required to find a set of k key nodes that would maximize the number of nodes being influenced in the network. The lambda-coverage problem is concerned with finding a set of k key nodes having minimal size that can influence a given percentage lambda of the nodes in the entire network. We propose a new way of solving these problems using the concept of Shapley value which is a well known solution concept in cooperative game theory. Our approach leads to algorithms which we call the ShaPley value-based Influential Nodes (SPINs) algorithms for solving the top-k nodes problem and the lambda-coverage problem. We compare the performance of the proposed SPIN algorithms with well known algorithms in the literature. Through extensive experimentation on four synthetically generated random graphs and six real-world data sets (Celegans, Jazz, NIPS coauthorship data set, Netscience data set, High-Energy Physics data set, and Political Books data set), we show that the proposed SPIN approach is more powerful and computationally efficient. Note to Practitioners-In recent times, social networks have received a high level of attention due to their proven ability in improving the performance of web search, recommendations in collaborative filtering systems, spreading a technology in the market using viral marketing techniques, etc. It is well known that the interpersonal relationships (or ties or links) between individuals cause change or improvement in the social system because the decisions made by individuals are influenced heavily by the behavior of their neighbors. An interesting and key problem in social networks is to discover the most influential nodes in the social network which can influence other nodes in the social network in a strong and deep way. This problem is called the target set selection problem and has two variants: 1) the top-k nodes problem, where we are required to identify a set of k influential nodes that maximize the number of nodes being influenced in the network and 2) the lambda-coverage problem which involves finding a set of influential nodes having minimum size that can influence a given percentage lambda of the nodes in the entire network. There are many existing algorithms in the literature for solving these problems. In this paper, we propose a new algorithm which is based on a novel interpretation of information diffusion in a social network as a cooperative game. Using this analogy, we develop an algorithm based on the Shapley value of the underlying cooperative game. The proposed algorithm outperforms the existing algorithms in terms of generality or computational complexity or both. Our results are validated through extensive experimentation on both synthetically generated and real-world data sets.

Determining Top K Nodes in Social Networks using the Shapley Value

In this paper, we consider the problem of selecting, for any given positive integer k, the top-k nodes in a social network, based on a certain measure appropriate for the social network. This problem is relevant in many settings such as analysis of co-authorship networks, diffusion of information, viral marketing, etc. However, in most situations, this problem turns out to be NP-hard. The existing approaches for solving this problem are based on approximation algorithms and assume that the objective function is sub-modular. In this paper, we propose a novel and intuitive algorithm based on the Shapley value, for efficiently computing an approximate solution to this problem. Our proposed algorithm does not use the sub-modularity of the underlying objective function and hence it is a general approach. We demonstrate the efficacy of the algorithm using a co-authorship data set from e-print arXiv (www.arxiv.org), having 8361 authors.

A Shapley Value Analysis to Coordinate the Formation of Procurement Networks

In this paper we address the problem of forming procurement networks for items with value adding stages that are linearly arranged. Formation of such procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions. Research in supply chain management has emphasized that such decisions need to take into account the fact that suppliers and buyers are intelligent and rational agents who act strategically. In this paper, we view the problem of procurement network formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a fair manner. We study the implications of using the Shapley value as a solution concept for forming such procurement networks. We also present a protocol, based on the extensive form game realization of the Shapley value, for forming these networks.

Influence limitation in multi-campaign social networks: A Shapley value based approach

We investigate the problem of influence limitation in the presence of competing campaigns in a social network. Given a negative campaign which starts propagating from a specified source and a positive/counter campaign that is initiated, after a certain time delay, to limit the the influence or spread of misinformation by the negative campaign, we are interested in finding the top k influential nodes at which the positive campaign may be triggered. This problem has numerous applications in situations such as limiting the propagation of rumor, arresting the spread of virus through inoculation, initiating a counter-campaign against malicious propaganda, etc. The influence function for the generic influence limitation problem is non-submodular. Restricted versions of the influence limitation problem, reported in the literature, assume submodularity of the influence function and do not capture the problem in a realistic setting. In this paper, we propose a novel computational approach for the influence limitation problem based on Shapley value, a solution concept in cooperative game theory. Our approach works equally effectively for both submodular and non-submodular influence functions. Experiments on standard real world social network datasets reveal that the proposed approach outperforms existing heuristics in the literature. As a non-trivial extension, we also address the problem of influence limitation in the presence of multiple competing campaigns.

Algoritmo de Gale-Shapley. Variaciones y alternativas

En esta memoria se trata el problema de encontrar un algoritmo que construya un emparejamiento entre dos grupos, entendiendo por emparejamiento la asignacion a cada individuo, de cada grupo, otro individuo. La situaci on inicial de la que parte el problema es la siguiente: Dos grupos, los proponentes y los propuestos, que est an formados por n individuos cada uno, siendo n la dimensi on del problema. El grupo de los proponentes es el encargado de hacer las propuestas a la hora de construir el emparejamiento. El grupo de los propuestos es el encargado de recibir y gestionar las propuestas a la hora de construir el emparejamiento. Cada individuo de cada grupo ordena en una lista, de manera decreciente, a individuos del otro grupo atendiendo a su preferencia a la hora de ser emparejado, a esta lista la llamaremos lista de preferencia del individuo, considerando el quedarse solo la opci on menos preferida de entre las aceptables. El objetivo del problema es crear un emparejamiento en el que cada pareja sea satisfactoria para los individuos que la crean en base a las preferencias de cada uno.