The cg-average tree value for games on cycle-free fuzzy communication structures

The main goal in a cooperative game is to obtain a fair allocation of the profit due the cooperation of the involved agents. The most known of these allocations is the Shapley value. This allocation considers that the communication among the players is complete. The Myerson value is a modification of the Shapley value considering a communication structure which determines the feasible bilateral relationships among the agents. This allocation of the profit is not always a stable solution. Another payoff allocation for games with a communication structure from the definition of the Shapley value is the average tree value. This one is a stable solution for any game using a cycle-free communication structure. Later fuzzy communication structures were introduced. In a fuzzy communication structure, the membership of the agents and the relationships among them are leveled. The Myerson value was extended in several different ways depending on the behavior of the agents. In this paper, the average tree value is extended to games with fuzzy communication structures taking one particular version: the Choquet by graphs (cg). We present an application to the management of an electrical network with an algorithmic implementation.Spanish Ministry of Education and Science MTM2017-83455-PAndalusian Government FQM23

Entropy of capacities on lattices and set systems

We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measures. Capacities on lattices address the general case where the family of subsets is not necessarily the Boolean lattice of all subsets. Our definition encompasses the classical definition of Shannon for probability measures, as well as the entropy of Marichal defined for classical capacities. Some properties and examples are given

Lattices and discrete methods in cooperative games and decisions

Questa tesi si pone l'obiettivo di presentare la teoria dei giochi, in particolare di quelli cooperativi, insieme alla teoria delle decisioni, inquadrandole formalmente in termini di matematica discreta. Si tratta di due campi dove l'indagine si origina idealmente da questioni applicative, e dove tuttavia sono sorti e sorgono problemi più tipicamente teorici che hanno interessato e interessano gli ambienti matematico e informatico. Anche se i contributi iniziali sono stati spesso formulati in ambito continuo e utilizzando strumenti tipici di teoria della misura, tuttavia oggi la scelta di modelli e metodi discreti appare la più idonea. L'idea generale è quindi quella di guardare fin da subito al complesso dei modelli e dei risultati che si intendono presentare attraverso la lente della teoria dei reticoli. Ciò consente di avere una visione globale più nitida e di riuscire agilmente ad intrecciare il discorso considerando congiuntamente la teoria dei giochi e quella delle decisioni. Quindi, dopo avere introdotto gli strumenti necessari, si considerano modelli e problemi con il fine preciso di analizzare dapprima risultati storici e solidi, proseguendo poi verso situazioni più recenti, più complesse e nelle quali i risultati raggiunti possono suscitare perplessità. Da ultimo, vengono presentate alcune questioni aperte ed associati spunti per la ricerca

Contributions to Game Theory and Management. Vol. III. Collected papers presented on the Third International Conference Game Theory and Management.

The collection contains papers accepted for the Third International Conference Game Theory and Management (June 24-26, 2009, St. Petersburg University, St. Petersburg, Russia). The presented papers belong to the field of game theory and its applications to management. The volume may be recommended for researches and post-graduate students of management, economic and applied mathematics departments.

The core of games on ordered structures and graphs

In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In many situations, this assumption is too strong and one has to deal with some unfeasible coalitions. Defining a game on a subcollection of the power set of the set of players has many implications on the mathematical structure of the core, depending on the precise structure of the subcollection of feasible coalitions. Many authors have contributed to this topic, and we give a unified view of these different results

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment

Mathematical Game Theory

These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person and, in particular, combinatorial and zero-sum games as well as models for investing and betting. n-person games are studied with emphasis on notions of utilities, potentials and equilibria, which allows to subsume cooperative games as special cases. The represenation of a game theoretic system in a Hilbert space furthermore establishes a link to the mathematical model of quantum mechancis and general interaction systems

Structuration des processus d'aide à la décision par analyse bipolaire

Le travail de recherche présenté dans ce mémoire s'inscrit dans le champ de l'aide à la décision multicritère. Ce champ aborde la décision dans un contexte où un groupe d'alternatives est évalué à travers un ensemble de critères (souvent contradictoires) afin d'estimer le potentiel de chacune à atteindre les objectifs fixés par un certain nombre de décideurs. La contribution de cette thèse concerne la structuration des problèmes d'aide à la décision par une approche bipolaire flexible qui permet d'évaluer les alternatives en distinguant leurs aspects positifs et négatifs vis-à-vis des objectifs à atteindre. Dans un premier temps, des modèles de structuration bipolaire sont proposés pour évaluer les problèmes de décision au niveau individuel. Les relations de synergie et les interactions potentielles entre les caractéristiques de la décision (attributs, alternatives, objectifs) sont modélisées dans un contexte bipolaire et intégrées à des approches de résolution tenant compte de l'environnement certain ou incertain dans lequel l'évaluation se déroule. Dans un deuxième temps, les décisions de groupe sont traitées en considérant l'impact du facteur humain (à travers les notions de peur, individualisme, influence, prudence, etc.) sur la capacité décisionnelle aux niveaux individuel et collectif. Des modèles d'évaluation et des techniques d'atteinte de consensus sont proposées pour deux catégories de problèmes relativement indépendants ; les problèmes de choix social et les jeux stratégiques.The research presented in this thesis concerns the multi-criteria decision support field. This field aims at helping decision makers (DM) to face decisions involving several conflicting objectives. To deals with this, decision is addressed in a context where a group of alternatives is evaluated through a set of criteria (often contradictory) to estimate the potential of each to achieve the goals. The main concern of this research is to propose flexible structuring decision problem support for evaluating alternatives distinguishing between positive and negative aspects they present with regard to objectives achievement. Bipolar structure models are proposed first to evaluate the decision problems at the individual level. The synergistic relationships and potential interactions between the decision characteristics (attributes, alternative objectives) are modeled in a bipolar context and integrated into resolution approaches taking account the certain or uncertain environment in which the evaluation takes place. In a second part, group decision problems are discussed taking into account the impact of human behaviour (influence, individualism, fear, caution, etc.) on decisional capacity at individual and collective levels. Valuation models and a consensus process are proposed in two relatively independent problem categories: social choice problems, and, strategic game problems