Complex economic activity often involves inter-relationships at several levels of production, often referred to as supply chains or procurement networks. In this thesis 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. Game theory has therefore emerged as a crucial tool for supply chain researchers to model, analyze, and design supply chains that are both efficient and stable. In this thesis, we explore cooperative game theory as a framework to model and analyze the formation of efficient and stable procurement networks. 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 address this problem in three different informational settings: (a) Complete information environments, (b) Incomplete but non-exclusive information environments and (c) Incomplete information environments. In the complete information case, we first investigate the use of the core as a solution concept. We show the structural conditions under which the core is non-empty. We then provide an extensive form game that implements the core in sub-game perfect Nash equilibrium whenever the core is non-empty. Secondly, we examine the implications of using the Shapley value as a solution concept for the game when the buyer is also included as a game theoretic agent. Analogous to the mechanism that implements the core, we adapt and construct an extensive form game to implement the Shapley value of the game. In the incomplete but non-exclusive information case, we focus on the incentive compatible coarse core as an appropriate solution concept and show its non-emptiness for the PNF game. In the incomplete information case, we focus on the incentive compatible fine core as an appropriate solution concept and show its non-emptiness for the PNF game. We believe the thesis establishes cooperative game theory as an extremely effective tool to model and solve the procurement network formation problem. 1

Le premier chapitre, en français, présente les principaux outils mathématiques utilisés dans le manuscrit, les résultats classiques sur la rationalité coalitionnelle pour les jeux coopératifs à utilité transférable et notamment sur le cœur et ses extensions, quelques résultats nouveaux sur le cœur k-additif et l’implémentation en équilibre de Nash fort de solutions de jeux coopératifs. Il y est synthétisé, sans démonstrations, les résultats des trois articles ainsi que quelques résultats nouveaux ou complémentaires. Les trois chapitres suivants, en anglais, correspondent aux trois articles. L’annexe A donnera en anglais les démonstrations des résultats nouveaux et non contenus dans les articles. / The first chapter, in french, presents the main mathematics tools used for this thesis, some classical results about coalitional rationality for cooperative TU-games, and among other things, about the core and its extensions. This chapter presents also some new or less known results about the k-additive core and strong Nash implementation of some cooperative games’ solutions. In addition, we summurize, without proofs, the main results which are contained in the three articles and some extra results that can be read in english in the appendix A. The three next chapters, in english, are the three articles. The Appendix A gives, in english, the proof of some extra results.

Water resource management is a multifaceted issue that becomes more complex when considering multiple nations’ interdependence upon a single shared transboundary river basin. With over 200 transboundary river basins worldwide shared by two or more countries, it is important to develop tools to allow riparian countries to cooperatively manage these shared and often limited water resources. Cooperative game theory provides tools for determining if cooperation can exist across jurisdictional boundaries through a suite of mathematical tools that measure the benefits of cooperation among basin stakeholders. Cooperative game theory is also useful for transboundary negotiation because it provides a range of solutions which will satisfy all players in the game and provides methods to fairly and equitably allocate the gains of that cooperation to all participating stakeholders, if that cooperation is shown to be possible. This dissertation applies cooperative game theory concepts to the Rio Grande/Bravo basin in North America as a case study. The Rio Grande/Bravo forms the 1,200 km border between the United States and Mexico. A comprehensive water resources planning model was developed for the basin including the major water users, water related infrastructure including reservoirs, and water policy logic related to the bi-national water sharing agreements. The water planning model is used to calculate the characteristic functions for the cooperative game analysis. For the Water Demand Reduction Game, the largest agricultural users, District 005, District 025 and the Texas Watermaster Section below Falcon were defined individual players. The cooperative analysis was between the individual players rather than the countries. In addition to the cooperative analysis, performance measures for water deliveries were calculated to determine if water delivery was improved to each player under the cooperative game. The results show that the amount of additional water to the downstream players may not be large enough to induce cooperation. The small amount of increase in water deliveries is related to the large system losses as the water travels downstream over a long distance and a division of water under the 1944 Treaty between the United States and Mexico. / text

This dissertation deals with consumption in Swedish households between 1913 and 2001. More specifically, it asks whose resources matter most in determining consumption patterns. As a second question, the dissertation also attempts to establish whether the fact that simple covariance between a spouse’s background variables implies that the spouse has any influence at all over the household’s consumption decisions. The theoretical background is mostly drawn from literature regarding intra-household allocations: on the one hand cooperative game theory and on the other hand sociological theory. Cooperative game theory establishes influence, say or power within the household as a function of the marriage’s or cohabitation’s alternative cost, i.e., the difference between the utility level for a married or cohabiting person as opposed to a single person. Sociological theory considers the contribution one makes to the total level of utility in the household, whether in the form of monetary income, household work or as something else. This is in part conceptualized as a difference between exit and voice. The dissertation’s statistical analysis uses three surveys of household expenditure conducted in 1913, 1952 and 1999-2001. They give us an excellent picture of what they actually purchased during that year. The sample sizes are 552, 596 and 3,501, respectively. The dissertation’s main result is that human capital is a previously underestimated determinant of influence in consumption decisions. As the female stock of human capital increases, so does her influence over the household’s consumption decisions. In an attempt to determine the level of democracy within households, the dissertation uses a complementary data source: a questionnaire called “The Swedish People 1955”. Here, one of the questions directed to females was whether they checked with their husbands before deciding on a purchase, as a measure of intra-household democracy. This was then regressed upon the female share of total income, ideological position and two forms of human capital, one general and one for household work. Both forms of human capital lead to democratic households, which is taken to mean that human capital is important not only because it increases labor opportunities in the event of divorce (exit) but also because it increases female voice.

This thesis consists of three empirical studies. The first study, Rationales to Language-in-Education Policies in Postcolonial Africa: Towards a Holistic Approach, considers two issues. First, it explores the factors affecting the choice of an LiE policy in 35 African countries. The results show that the countries adopting a unilingual education system put different weights on the influential parameters than countries adopting a bilingual education system. Second, the study investigates how decision makers can ensure the optimal choice of language(s) of instruction by developing a non-cooperative game theoretic model with network externalities. The model shows that it is never optimal for two countries to become bilingual, or for the majority linguistic group to learn the language of the minority group, unless there is minimum cooperation to ensure an equitable redistribution of payoffs. The second study, The Role of Language in Learning Achievement: A Namibian Case Study, investigates the role played by home language and language proficiency on SACMEQ II mathematics scores of Namibian Grade-6 learners. HLM is used to partition the total variance in mathematics achievement into its within- and between-school components. Results show that although home language plays a limited role in explaining within- and between-school variations in mathematics achievement, language proficiency (proxied by reading scores) plays a significant role in the heterogeneity of results. Finally, the third study, Language Skills and Economic Returns, investigates the economic returns to language skills, assuming that language competencies constitute key components of human capital. It presents results from eight IALS countries. The study finds that in each country, skills in a second language are a significant factor that constrains wage opportunities positively.

A comprehensive model named the Cooperative Water Allocation Model (CWAM) is developed for modeling equitable and efficient water allocation among competing users at the basin scale, based on a multiperiod node-link river basin network. The model integrates water rights allocation, efficient water allocation and equitable income distribution subject to hydrologic constraints comprising both water quantity and quality considerations. CWAM allocates water resources in two steps: initial water rights are firstly allocated to water uses based on legal rights systems or agreements, and then water is reallocated to achieve efficient use of water through water transfers. The associated net benefits of stakeholders participating in a coalition are allocated by using cooperative game theoretical approaches. <br /><br /> The first phase of the CWAM methodology includes three methods for deriving initial water rights allocation among competing water uses, namely the priority-based multiperiod maximal network flow (PMMNF) programming, modified riparian water rights allocation (MRWRA) and lexicographic minimax water shortage ratios (LMWSR) methods. PMMNF is a very flexible approach and is applicable under prior, riparian and public water rights systems with priorities determined by different criteria. MRWRA is essentially a special form of PMMNF adapted for allocation under the riparian regime. LMWSR is designed for application under a public water rights system, which adopts the lexicographic minimax fairness concept. The second step comprises three sub-models: the irrigation water planning model (IWPM) is a model for deriving benefit functions of irrigation water; the hydrologic-economic river basin model (HERBM) is the core component of the coalition analysis, which searches for the values of various coalitions of stakeholders and corresponding optimal water allocation schemes, based on initial water rights, monthly net benefit functions of demand sites and the ownership of water uses; the sub-model cooperative reallocation game (CRG) of the net benefit of the grand coalition adopts cooperative game solution concepts, including the nucleolus, weak nucleolus, proportional nucleolus, normalized nucleolus and Shapley value, to perform equitable reallocation of the net benefits of stakeholders participating in the grand coalition. The economically efficient use of water under the grand coalition is achieved through water transfers based on initial water rights. <br /><br /> Sequential and iterative solution algorithms utilizing the primal simplex method are developed to solve the linear PMMNF and LMWSR problems, respectively, which only include linear water quantity constraints. Algorithms for nonlinear PMMNF and LMWSR problems adopt a two-stage approach, which allow nonlinear reservoir area- and elevation-storage relations, and may include nonlinear water quality constraints. In the first stage, the corresponding linear problems, excluding nonlinear constraints, are solved by a sequential or iterative algorithm. The global optimal solution obtained by the linear programming is then combined together with estimated initial values of pollutant concentrations to be used as the starting point for the sequential or iterative nonlinear programs of the nonlinear PMMNF or LMWSR problem. As HERBM adopts constant price-elasticity water demand functions to derive the net benefit functions of municipal and industrial demand sites and hydropower stations, and quadratic gross benefit functions to find the net benefit functions of agriculture water uses, stream flow demands and reservoir storages, it is a large scale nonlinear optimization problem even when the water quality constraints are not included. An efficient algorithm is built for coalition analysis, utilizing a combination of the multistart global optimization technique and gradient-based nonlinear programming method to solve a HERBM for each possible coalition. <br /><br /> Throughout the study, both the feasibility and the effectiveness of incorporating equity concepts into conventional economic optimal water resources management modeling are addressed. The applications of CWAM to the Amu Darya River Basin in Central Asia and the South Saskatchewan River Basin in western Canada demonstrate the applicability of the model. It is argued that CWAM can be utilized as a tool for promoting the understanding and cooperation of water users to achieve maximum welfare in a river basin and minimize the damage caused by water shortages, through water rights allocation, and water and net benefit transfers among water users under the regulated water market or administrative allocation mechanism.

A comprehensive model named the Cooperative Water Allocation Model (CWAM) is developed for modeling equitable and efficient water allocation among competing users at the basin scale, based on a multiperiod node-link river basin network. The model integrates water rights allocation, efficient water allocation and equitable income distribution subject to hydrologic constraints comprising both water quantity and quality considerations. CWAM allocates water resources in two steps: initial water rights are firstly allocated to water uses based on legal rights systems or agreements, and then water is reallocated to achieve efficient use of water through water transfers. The associated net benefits of stakeholders participating in a coalition are allocated by using cooperative game theoretical approaches. <br /><br /> The first phase of the CWAM methodology includes three methods for deriving initial water rights allocation among competing water uses, namely the priority-based multiperiod maximal network flow (PMMNF) programming, modified riparian water rights allocation (MRWRA) and lexicographic minimax water shortage ratios (LMWSR) methods. PMMNF is a very flexible approach and is applicable under prior, riparian and public water rights systems with priorities determined by different criteria. MRWRA is essentially a special form of PMMNF adapted for allocation under the riparian regime. LMWSR is designed for application under a public water rights system, which adopts the lexicographic minimax fairness concept. The second step comprises three sub-models: the irrigation water planning model (IWPM) is a model for deriving benefit functions of irrigation water; the hydrologic-economic river basin model (HERBM) is the core component of the coalition analysis, which searches for the values of various coalitions of stakeholders and corresponding optimal water allocation schemes, based on initial water rights, monthly net benefit functions of demand sites and the ownership of water uses; the sub-model cooperative reallocation game (CRG) of the net benefit of the grand coalition adopts cooperative game solution concepts, including the nucleolus, weak nucleolus, proportional nucleolus, normalized nucleolus and Shapley value, to perform equitable reallocation of the net benefits of stakeholders participating in the grand coalition. The economically efficient use of water under the grand coalition is achieved through water transfers based on initial water rights. <br /><br /> Sequential and iterative solution algorithms utilizing the primal simplex method are developed to solve the linear PMMNF and LMWSR problems, respectively, which only include linear water quantity constraints. Algorithms for nonlinear PMMNF and LMWSR problems adopt a two-stage approach, which allow nonlinear reservoir area- and elevation-storage relations, and may include nonlinear water quality constraints. In the first stage, the corresponding linear problems, excluding nonlinear constraints, are solved by a sequential or iterative algorithm. The global optimal solution obtained by the linear programming is then combined together with estimated initial values of pollutant concentrations to be used as the starting point for the sequential or iterative nonlinear programs of the nonlinear PMMNF or LMWSR problem. As HERBM adopts constant price-elasticity water demand functions to derive the net benefit functions of municipal and industrial demand sites and hydropower stations, and quadratic gross benefit functions to find the net benefit functions of agriculture water uses, stream flow demands and reservoir storages, it is a large scale nonlinear optimization problem even when the water quality constraints are not included. An efficient algorithm is built for coalition analysis, utilizing a combination of the multistart global optimization technique and gradient-based nonlinear programming method to solve a HERBM for each possible coalition. <br /><br /> Throughout the study, both the feasibility and the effectiveness of incorporating equity concepts into conventional economic optimal water resources management modeling are addressed. The applications of CWAM to the Amu Darya River Basin in Central Asia and the South Saskatchewan River Basin in western Canada demonstrate the applicability of the model. It is argued that CWAM can be utilized as a tool for promoting the understanding and cooperation of water users to achieve maximum welfare in a river basin and minimize the damage caused by water shortages, through water rights allocation, and water and net benefit transfers among water users under the regulated water market or administrative allocation mechanism.

In this thesis a known heuristic for decreasing a node's centrality scores while maintaining influence, called ROAM, is compared to a modified version specifically designed to decrease eigenvector centrality. The performances of these heuristics are also tested against the Shapley values of a cooperative game played over the considered network, where the game is such that influential nodes receive higher Shapley values. The modified heuristic performed at least as good as the original ROAM, and in some instances even better (especially when the terrorist network behind the World Trade Center attacks was considered). Both heuristics increased the influence score for a given targeted node when applied consecutively on the WTC network, and consequently the Shapley values increased as well. Therefore the Shapley value of the game considered in this thesis seems to be well suited for discovering individuals that are assumed to actively trying to evade social network analysis.

Diese Dissertation präsentiert Modelle zur Lösung von Verhandlungsproblemen mit diskreten Strukturen. Hauptgrundlage der Betrachtung ist dabei die Erweiterung und Anwendung von Theorien der kooperativen Spieltheorie. Insbesondere der Shapley-Wert spielt eine wichtige Rolle. Als erste Problemklasse werden kooperative Spiele präsentiert, bei denen einige Spiele feste Auszahlungen erhalten. Als zweite Problemklasse werden kooperative Spiele untersucht, deren Lösungen ausschließlich ganzzahlig sein dürfen.

Au cours des vingt dernières années, le secteur des services est devenu le secteur le plus important en nombre d'actifs occupés dans l’économie mondiale, en particulier dans les pays développés. Par ailleurs, la concurrence et la coopération dans le secteur des services sont devenues de plus en plus populaires dans le contexte de la mondialisation économique. Comment collaborer avec un accord gagnant-gagnant apporte une source fertile de problèmes de management des opérations dans le domaine des services. Dans cette thèse, nous étudions des stratégies de collaboration dans des systèmes de services homogènes. Nous nous concentrons en particulier sur les stratégies de pooling des ressources de service.Dans les deux premières parties, nous étudions le problème de partage des coûts entre les fournisseurs de services indépendants avec des temps de service qui suivent une distribution générale et en tenant compte de l'abandon des clients. Nous modélisons à la fois chaque fournisseur de services et la coalition coopérative comme des files d'attente avec serveur unique, et spécialisons les stratégies de pooling avec les capacités de services fixes et modifiables. Dans la dernière partie, nous abordons le problème de pooling dans le cadre multiserveur pour évaluer la qualité de l'hypothèse "superserveur". Nous étudions numériquement l'impact de la variabilité de la durée de service et l'abandon des clients sur les jeux de mise en commun des ressources. Nous comparons aussi les partages des coûts entre le système de "super-serveur" et multiserveur. / In past twenty years, the service sector has emerged as the primary sector in the world economy, especially in developed countries. Competition and cooperation in service industries have become more and more popular in the context of economic globalization. How to operate the collaboration with a win-win agreement brings a fertile source of operations management issues in service science. In this thesis, we study collaborations between homogeneous service systems in terms of resource pooling strategies.In the first two parts, we investigate the cost-sharing problem among independent service providers with general service times and accounting for the customer abandonment. We model both the service provider and the cooperative coalition as single server queues, and specialize the capacity pooling strategies with the fixed and optimized service capacities.Finally, we address the service pooling problem in the multi-serverpooling setting to assess the quality of the "super-server" assumption.We numerically investigate the impact of service duration variability and customer abandonment on the pooling game. We compare between cost-sharing results of the two resource pooling concepts, with or without the "super-server" assumptions.