One problem in cooperative game theory is to model situations when two players refuse to cooperate (or the problem of quarreling members in coalitions). One example of such exclusions is the coalition statements of parliamentary parties. Other situations in which incompatible players affect the outcome are teams in firms and markets, for example. To model these exclusions in cooperative game theory, the excluded coalitions value ( φE value) was introduced. This value is based on the Shapley value and takes into account that players exclude coalitions with other players. In this article, we deduce some properties of this new value. After some general results, we analyze the apex game that could be interpreted as a team situation and the glove game that models markets where sellers and buyers deal. For team situations, we show that all employees have a common interest for cooperation. On asymmetric markets, excluding coalitions affect the market players of the scarce side to a higher extent.

Cette thèse traite de l’analyse théorique et l’application d’une nouvelle famille de jeux coopératifs, où la valeur de chaque coalition peut être calculée à partir des contributions des joueurs par un opérateur additif qui décrit comme les capacités individuelles interagissent au sein de groupes. Précisément, on introduit une grande classe de jeux, les Generalized Additive Games, qui embrasse plusieurs classes de jeux coopératifs dans la littérature, et en particulier de graph games, où un réseau décrit les restrictions des possibilités d’interaction entre les joueurs. Des propriétés et solutions pour cette classe de jeux sont étudiées, avec l’objectif de fournir des outils pour l’analyse de classes de jeux connues, ainsi que pour la construction de nouvelles classes de jeux avec des propriétés intéressantes d’un point de vue théorique. De plus, on introduit une classe de solutions pour les communication situations, où la formation d’un réseau est décrite par un mécanisme additif, et dans la dernière partie de cette thèse on présente des approches avec notre modèle à des problèmes réels modélisés par des graph games, dans les domaines de la théorie de l’argumentation et de la biomédecine. / This thesis deals with the theoretical analysis and the application of a new family of cooperative games, where the worth of each coalition can be computed from the contributions of single players via an additive operator describing how the individual abilities interact within groups. Specifically, we introduce a large class of games, namely the Generalized Additive Games, which encompasses several classes of cooperative games from the literature, and in particular of graph games, where a network describes the restriction of the interaction possibilities among players. Some properties and solutions of such class of games are studied, with the objective of providing useful tools for the analysis of known classes of games, as well as for the construction of new classes of games with interesting properties from a theoretic point of view. Moreover, we introduce a class of solution concepts for communication situations, where the formation of a network is described by means of an additive pattern, and in the last part of the thesis we present two approaches using our model to real-world problems described by graph games, in the fields of Argumentation Theory and Biomedicine.

[pt] Minerar bitcoins é uma atividade incerta, e para realizá-la, os participantes competem em um processo chamado Proof-Of-Work. Cada participante pode passar meses ou até anos sem fluxos positivos de caixa, enquanto os custos se mantém. Isto pode afastá-los da tecnologia e a saída de membros afeta a própria rede, que não sobrevive sem a presença de mineradores. Este trabalho propõe estudar o compartilhamento de recompensas em estruturas já existentes na rede: mineradores se juntando em pools de mineração e dividindo receitas e custos, assim diminuindo a variabilidade e gerando fluxos positivos de caixa mais constantes. A receita e custos são modelados, e um modelo de programação estocástica é proposto para encontrar as alocações ótimas que garantem a permanência dos membros no pool. Este grupo de é caracterizado por uma coalizão, estudado através de Teoria dos Jogos. O comportamento dos jogadores também é de estudo neste trabalho, e uma medida monetária de risco, na forma de CVaR (Conditional Value at Risk) é usada para representar o perfil de risco do minerador e as consequências para as alocações ótimas. Embora não haja benefício estrito em fazer parte do pool para um único período de análise, há ganho financeiro quando se analisa em múltiplos períodos, e o tempo médio para se acertar um hash diminui quando os participantes se juntam em um pool. Um ganho na probabilidade de mineração ao fazer parte de um pool aumentaria a receita média da coalizão, trazendo ganhos financeiros mesmo em um único período de análise. Divisões intuitivas de recursos, como por poder computacional ou igualitária podem não garantir estabilidade do pool, principalmente considerando períodos longos de tempo. Tal estabilidade é possível em um futuro sem receitas fixas de mineração, se ocorrerem também mudanças nas receitas variáveis e custos. Três funções objetivo diferentes representando três idéias de partilha de recompensa são comparadas e uma metodologia é proposta para uso conjunto de pelo menos duas destas, com objetivo de aumentar a justiça na divisão das recompensas. / [en] Mining Bitcoins is an uncertain activity, and to perform it, players must compete in a process known as Proof-Of-Work. A miner may spend months or even years without positive cash flows on this process, while still incurring in the associated costs. This outcome has the possibility to drive them away from the technology, and the departure of members affects the network itself, as it cannot survive without the presence of miners. This work proposes to study the sharing of rewards in structures already presented in the network: miners joining forces and taking place in mining pools, sharing revenues and costs, thus having positive cash flows more often, reducing variability in gains. The revenues and costs are modeled, and a stochastic optimization model is proposed to find the optimal allocations that guarantee that all members stay within the pool. This group of miners is characterized by a coalition, studied through Game Theory. The behavior of the players is also subject of this study, and a monetary risk measure, by the form of CVaR (Conditional Value at Risk) is used to represent the miner s risk profile and consequences to the optimal allocations. While there is no strict benefit from being part of a pool for a single block, there is financial gain when looking at multi-period, and the average time to correctly guess a hash decreases when players join forces in a pool. A gain in mining probability by being in the pool would raise the average reward of the coalition and allow for financial benefit even in single period.We observe that intuitive sharing allocations such as through computational power and equally dividing rewards may not guarantee the stability of the pool, mainly when longer periods of time are considered. Said stability is possible in the future without fixed incomes, but with changes to the variable rewards and the costs of mining. Lastly, three different objective functions representing three ideas to share the rewards within the nucleolus are compared and a method is proposed to collectively use at least two of them, aiming increased fairness in the sharing of rewards.

In contexts involving multiple agents (players), determining how they can cooperate through the formation of coalitions and how they can share surplus benefits coming from the collaboration is crucial. This can provide decision-aid to players and analysis tools for policy makers regulating economic markets. Such settings belong to the field of cooperative game theory. A critical element in this area has been the size of the representation of these games: for each possible partition of players, the value of each coalition on it must be provided. Symmetric partition function form games (SPFGs) belong to a class of cooperative games with two important characteristics. First, they account for externalities provoked by any group of players joining forces or splitting into subsets on the remaining coalitions of players. Second, they consider that players are indistinct, meaning that only the number of players in each coalition is relevant for the SPFG. Using mixed-integer programming, we present the first representation of SPFGs that is polynomial on the number of players in the game. We also characterize the family of SPFGs that we can represent. In particular, the representation is able to encode exactly all SPFGs with five players or less. Furthermore, we provide a compact representation approximating SPFGs when there are six players or more and the SPFG cannot be represented exactly. We also introduce a flexible framework that uses stability methods inspired from the literature to identify a stable social-welfare maximizing game outcome using our representation. We showcase the value of our compact (approximated) representation and approach to determine a stable partition and payoff allocation to a competitive market from the literature. / Dans tout contexte impliquant plusieurs agents (joueurs), il est impératif de déterminer comment les agents coopéreront par la formation de coalitions et comment ils partageront les bénéfices supplémentaires issus de la collaboration. Ceci peut fournir une aide à la décision aux joueurs, ou encore des outils d'analyse pour les responsables en charge de réguler les marchés économiques. De telles situations relèvent de la théorie des jeux coopérative. Un élément crucial de ce domaine est la taille de la représentation de ces jeux : pour chaque partition de joueurs possible, la valeur de chaque coalition qu'on y retrouve doit être donnée. Les jeux symétriques à fonction de partition (SPFG) appartiennent à une classe de jeux coopératifs possédant deux caractéristiques principales. Premièrement, ils sont sensibles aux externalités, provoquées par n'importe quel groupe de joueurs qui s'allient ou défont leurs alliances, qui sont ressenties par les autres coalitions de joueurs. Deuxièmement, ils considèrent que les joueurs sont indistincts, et donc que seul le nombre de joueurs dans chaque coalition est à retenir pour représenter un SPFG. Par l'utilisation d'outils de programmation mixte en nombres entiers, nous présentons la première représentation de SPFG qui est polynomiale en nombre de joueurs dans le jeu. De surcroît, nous caractérisons la famille des SPFG qu'il est possible de représenter, qui inclut notamment tous les SPFG de cinq joueurs ou moins. De plus, elle dispose d'une approximation compacte pour le cas où, dans un jeu à six joueurs ou plus, le SPFG ne peut pas être représenté de façon exacte. Également, nous introduisons un cadre flexible qui utilise des méthodes visant la stabilité inspirées par la littérature pour identifier, à l'aide de notre représentation, une issue stable qui maximise le bien-être social des joueurs. Nous démontrons la valeur de notre représentation (approximée) compacte et de notre approche pour sélectionner une partition stable et une allocation des profits dans une application de marché compétitif provenant de la littérature.

Plusieurs pays possèdent des programmes de don croisé de rein (PDCR). Le but de ces programmes est d’aider les patients ayant un donneur incompatible à obtenir une greffe, en échangeant les donneurs incompatibles entre les patients. Pour pouvoir obtenir des bassins de paires incompatibles de plus grande taille, il est possible d’élargir les PDCR pour y inclure plusieurs pays ou hôpitaux. Par contre, on doit s’attendre à ce que ces derniers agissent de façon stratégique pour maximiser le nombre de leurs patients obtenant une greffe. Avec ce cadre, on peut définir le problème de don croisé de rein à plusieurs agents. Dans ce mémoire, nous modélisons ce problème comme un jeu coopératif à utilité non- transférable et nous présentons le noyau faible comme solution à ce jeu. Nous étudions empiriquement notre solution sur des exemples basés sur des données réelles et montrons qu’elle est atteignable en pratique. Nous comparons aussi le noyau faible à une autre solution présente dans la littérature: les couplages résistants aux rejets. / In various countries, kidney paired donation programs (KPDs) are implemented. These programs aim to help patients with an incompatible donor to obtain a transplant by swapping the donors between the patients. In order to increase the size of the pool of incompatible patient-donor pairs and potentially enhance patient benefits, KPDs can be extended to include multiple countries or hospitals. However, unlike existing nationwide KPDs, strategic behaviour from these entities (agents) is to be expected. This gives rise to the multi-agent kidney exchange problem. In this work, we model for the first time this problem as a non-transferable utility game. We also propose and argue in favour of the use of the weak core as a solution concept for the game. Using integer programming tools, we empirically study our solution concept on instances from the literature, which are derived from real-world data, and show that it is attainable in practice. We also compare the weak core to another recently presented solution concept from the literature, the rejection-proof matching.

[EN] Adaptation to the multiple facets of global change challenges the conventional means of sustainably planning and managing water resources at the river basin scale. Numerous demand or supply management options are available, from which adaptation measures need to be selected in a context of high uncertainty of future conditions. Given the interdependency of water users, agreements need to be found at the local level to implement the most effective adaptation measures. Therefore, this thesis develops an approach combining economics and water resources engineering to select a cost-effective programme of adaptation measures in the context of climate change uncertainty, and to define an equitable allocation of the cost of the adaptation plan between the stakeholders involved. A framework is developed to integrate inputs from the two main approaches commonly used to plan for adaptation. The first, referred to as "top-down", consists of a modelling chain going from global greenhouse gases emission scenarios to local hydrological models used to assess the impact of climate change on water resources. Conversely, the second approach, called "bottom-up", starts from assessing vulnerability at the local level to then identify adaptation measures used to face an uncertain future. Outcomes from these two approaches are integrated to select a cost-effective combination of adaptation measures through a least-cost optimization model developed at the river basin scale. The model is then used to investigate the trade-offs between different planning objectives defined in terms of environmental flow requirements, irrigated agriculture development, and the cost of the programme of measures. The performances of a programme of measures are finally assessed under different climate projections to identify robust and least-regret adaptation measures. The issue of allocating the cost of the adaptation plan is considered through two complementary perspectives. The outcome of a negotiation process between the stakeholders is modelled through the implementation of cooperative game theory to define cost allocation scenarios. These results are compared with cost allocation rules based on social justice principles to provide contrasted insights into a negotiation process. This innovative framework has been applied in a Mediterranean case study in the Orb River basin (France). Mid-term climate projections, downscaled from 9 General Climate Models, are used to assess the uncertainty associated with climate projections. Demand evolution scenarios have been developed to project agricultural and urban water demands on the 2030 time horizon. The least-cost river basin optimization model developed in GAMS allows the cost-effective selection of a programme of measures from a catalogue of 462 supply and demand management measures. Nine cost allocation scenarios based on different social justice principles have been discussed through face-to-face semi-structured interviews with 15 key informants and compared with solution concepts from cooperative game theory for a 3-player game defined at the river basin scale. The interdisciplinary framework developed in this thesis combines economics and water resources engineering methods, establishing a promising means of bridging the gap between bottom-up and top-down approaches and supporting the creation of cost-effective and equitable adaptation plans at the local level. / [ES] La adaptación a los múltiples aspectos del cambio global supone un reto para los enfoques convencionales de planificación y gestión sostenible de los recursos hídricos a escala de cuenca. Numerosas opciones de gestión de la demanda o de la oferta están disponibles, de entre las cuales es necesario seleccionar medidas de adaptación en un contexto de elevada incertidumbre sobre las condiciones futuras. Dadas las interdependencias existentes entre los usuarios del agua a nivel local, hace falta buscar acuerdos a escala de cuenca para implementar las medidas de adaptación más eficaces. Por este motivo, esta tesis desarrolla una metodología que, combinando economía e ingeniería de los recursos hídricos, busca seleccionar un programa de medidas coste-eficaz frente a las incertidumbres del cambio climático, y asimismo definir un reparto justo del coste de la adaptación entre los actores implicados. El marco metodológico ha sido desarrollado para integrar contribuciones de los dos principales enfoques utilizados para la planificación de la adaptación. El primero, denominado descendente ("top-down"), consiste en una cadena de modelación que va desde los escenarios de emisiones de gases efecto invernadero a nivel global hasta los modelos hidrológicos utilizados a nivel local para evaluar así el impacto del cambio climático sobre los recursos hídricos. Por el contrario, el segundo enfoque denominado ascendente ("bottom-up") empieza por evaluar la vulnerabilidad del sistema a nivel local para después identificar medidas de adaptación frente a un futuro incierto. Los resultados de los métodos mencionados previamente se han integrado con el fin de seleccionar una combinación coste-eficaz de medidas de adaptación a través de un modelo de optimización a menor coste a escala de cuenca. El modelo se utiliza para investigar las soluciones de compromiso ("trade-offs") entre diversos objetivos de planificación como son los caudales ecológicos necesarios, el desarrollo del regadío y el coste del programa de medidas. Seguidamente, se han evaluado los programas de adaptación frente a varias condiciones climáticas para definir así un programa de medidas robusto y de arrepentimiento mínimo frente al cambio climático. En la última parte se aborda el problema del reparto justo de los costes del plan de adaptación, entendiendo que esto es una manera de favorecer su implementación. Para ello, se han modelado los resultados de un proceso de negociación entre los diferentes actores mediante escenarios de reparto basados en la teoría de juegos cooperativos. Posteriormente, se han comparado estos resultados con otras reglas de reparto de costes basadas en principios de justicia social, proporcionando así un punto de vista diferente al proceso de negociación. Este novedoso enfoque ha sido aplicado a una cuenca mediterránea, la cuenca del rio Orb (Francia). Para ello, se han empleado proyecciones climáticas a medio-plazo de datos reescalados de 9 Modelos de Circulación Global. Además, se han desarrollado escenarios de evolución de la demanda en los sectores urbano y agrícola para el horizonte de planificación de 2030. El modelo de optimización a menor coste a escala de cuenca desarrollado en GAMS permite seleccionar un programa de medidas, de entre las 462 medidas de gestión de la oferta o de la demanda. Nueve escenarios de reparto de costes basados en diferentes principios de justicia social han sido debatidos con informantes clave mediante entrevistas y comparados con conceptos de solución de la teoría de juegos cooperativos, considerando un juego de 3 jugadores a escala de cuenca. El marco interdisciplinario desarrollado durante esta tesis combina métodos de economía y de ingeniería de los recursos hídricos de manera prometedora y permite integrar los enfoques "top-down" y "bottom-up", contribuyendo a definir un plan de adaptación coste-eficaz y justo a nivel local. / [CA] L'adaptació als múltiples aspectes del canvi global implica un repte per als enfocaments convencionals de planificació i gestió sostenible dels recursos hídrics a escala de conca. Existeixen nombroses opcions de gestió de la demanda y de la oferta. De entre elles, cal seleccionar mesures d'adaptació en un context d'incertesa elevada sobre les condicions futures. Donades les interaccions entre els usuaris de l'aigua a nivell local, és necessari buscar acords a escala de conca per tal d'implementar les mesures d'adaptació més eficaces. Per aquest motiu, la tesi desenvolupa una metodologia que, mitjançant la combinació d'economia i enginyeria dels recursos hídrics, siga adient per seleccionar un programa de mesures cost-eficaç per a fer front a les incerteses del canvi climàtic i, a més a més, definir un repartiment just del cost d'adaptació entre els actors implicats. El marc metodològic ha estat desenvolupat amb el fi de permetre integrar contribucions del principals enfocaments que s'utilitzen per a la planificació de l'adaptació. El primer, que es denomina descendent ("top-down"), consisteix a una cadena de modelació que va des dels escenaris d'emissions de gas d'efecte hivernacle a nivell global fins als models hidrològics a nivell local per avaluar l'impacte del canvi climàtic sobre els recursos hídrics. Per contra, el segon enfocament, que es denomina ascendent ("bottom-up"), comença per avaluar la vulnerabilitat del sistema a nivell local per a tot seguit identificar mesures d'adaptació de cara a un futur incert. Els resultats del mètodes esmentats prèviament, s'han integrat per a seleccionar una combinació de mesures d'adaptació cost-eficaç mitjançant un model d'optimització a menor cost a escala de conca. El model s'utilitza per investigar les solucions de compromís ("trade-offs") entre els diversos objectius de planificació, com són els cabals ecològics necessaris, el desenvolupament del regadiu i el cost del programa de mesures. A continuació, s'avaluen els programes d'adaptació per a varies condicions climàtiques amb el fi de definir un programa de mesures robust i de penediment mínim per a fer front al canvi climàtic. En la darrera part, s'escomet el problema del repartiment just dels costs del pla d'adaptació, considerant que això és una manera de facilitar la implementació del pla. En conseqüència, els resultats d'un procés de negociació entre els diferents actors han estat modelats mitjançant escenaris de repartiment basats en la teoria de jocs cooperatius. Tot seguit, els resultats s'han comparat amb altres regles de repartiment de costos basades en principis de justícia social. Això ha proporcionat un punt de vista diferent al procés de negociació. Aquest enfocament innovador s'ha aplicat a una conca mediterrània, la conca del riu Orb (França). Amb aquesta finalitat s'han utilitzat projeccions climàtiques a mig termini de dades reescalades de 9 Models de Circulació Global (MCG). A més a més, s'han desenvolupat escenaris d'evolució de la demanada en els sectors agrícola i urbà per a l'horitzó de planificació de 2030. El model d'optimització a menor cost a escala de conca desenvolupat en GAMS permet seleccionar un programa de mesures, de entre les 462 mesures de gestió de la oferta o de la demanda. Els nou escenaris de repartiment de costs han estat debatuts amb informants clau, mitjançant entrevistes, i comparats amb conceptes de solució de la teoria de jocs cooperatius, considerant un joc de 3 jugadors a escala de conca. El marc interdisciplinari desenvolupat al llarg de la tesi combina mètodes d'economia i d'enginyeria dels recursos hídrics de manera prometedora i permet la integració d'enfocaments "top-down" i "bottom-up", fet que contribueix a definir un pla d'adaptació cost-eficaç i just a escala local. / Girard, CDP. (2015). Integrating top-down and bottom-up approaches to design a cost-effective and equitable programme of measures for adaptation of a river basin to global change [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/59461 / Premios Extraordinarios de tesis doctorales