A cooperative game approach to a production planning problem

This paper deals with a production planning problem formulated as a Mixed Integer Linear Programming (MILP) model that has a competition component, given that the manufacturers are willing to produce as much products as they can in order to fulfil the market’s needs. This corresponds to a typical game theoretic problem applied to the productive sector, where a global optimization problem involves production planning in order to maximize the utilities for the different firms that manufacture the same type of products and compete in the market. This problem has been approached as a cooperative game, which involves a possible cooperation scheme among the manufacturers. The general problem was approached by Owen (1995) as the “production game” and the core was considered. This paper identifies the cooperative game theoretic model for the production planning MILP optimization problem and Shapley Value was chosen as the solution approach. The results obtained indicate the importance of cooperating among competitors. Moreover, this leads to economic strategies for small manufacturing companies that wish to survive in a competitive environment

What factors determine the number of trading partners?

The purpose of the paper is to provide a simple model explaining buyer-supplier relationships and show what factors determine the number of trading partners. We show that when the supplier is able to determine the number of trading partners, the optimal number is small if the supplier's bargaining power with them is weak, the economy of scope in the supplier's variable costs is significant, and that in its sunk investment is weak. Investment may be greater when the number of trading partners is small. The results may be consistent with the formation of Japanese buyer-supplier relations.

Incentive Design and Profit Sharing in Multi-modal Transportation Network

We consider the situation where multiple transportation service providers cooperate to offer an integrated multi-modal platform to enhance the convenience to the passengers through ease in multi-modal journey planning, payment, and first and last mile connectivity. This market structure allows the multi-modal platform to coordinate profits across modes and also provide incentives to the passengers. Accordingly, in this paper, we use cooperative game theory coupled with the hyperpath-based stochastic user equilibrium framework to study such a market. We assume that the platform sets incentive (subsidy or tax) along every edge in the transportation network. We derive the continuity and monotonicity properties of the equilibrium flow with respect to the incentives along every edge. The optimal incentives that maximize the profit of the platform are obtained through a two time-scale stochastic approximation algorithm. We use the asymmetric Nash bargaining solution to design a fair profit sharing scheme among the service providers. We show that the profit for each service provider increases after cooperation on such a platform. We complement the theoretical results through two numerical simulations

Coalition Formation in Games with Externalities

This paper studies an extensive form game of coalition formation with random proposers in games with externalities. It is shown that an agreement will be reached without delay if any set of coalitions profits from merging. Even under this strong condition, the equilibrium coalition structure is not necessarily efficient. There may be multiple equilibria even in the absence of externalities, and symmetric players are not necessarily treated symmetrically in equilibrium. If the grand coalition forms without delay in equilibrium, expected payoffs must be in the core of the characteristic function game that assigns to each coalition its equilibrium payoff. Compared with the rule of order process of Ray and Vohra (Games Econ Behav 26:286–336, 1999), the bargaining procedure with random proposers tends to give a large advantage to the proposer, whereas the bargaining procedure with a rule of order tends to favor the responders. The equilibria of the two procedures cannot be ranked in general in terms of efficiency

The Nash bargaining solution in general n-person cooperative games

We present a noncooperative foundation for the Nash bargaining solution for an n-person cooperative game in strategic form. The Nash bargaining solution should be immune to any coalitional deviations. Our noncooperative approach yields a new core concept, called the Nash core, for a cooperative game based on a consistency principle. We prove that the Nash bargaining solution can be supported (in every subgame) by a stationary subgame perfect equilibrium of the bargaining game if and only if the Nash bargaining solution belongs to the Nash core.Nash bargaining solution Noncooperative bargaining Coalition Externality Core n-Person cooperative games

Multi-objective cooperated operation of reservoirs : a case Study in the rio Tietê basin

Orientador: Alberto Luiz FrancatoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: A operação de reservatórios envolve um grande número de variáveis de decisão, as quais se arranjam para atender a um ou mais objetivos. Uma decisão que contempla mais de um objetivo pode ser estabelecida de acordo com as preferências do decisor, porém decisões de alta complexidade e impacto são mais defensáveis quando podem ser subsidiadas por modelos matemáticos de auxílio à tomada de decisão. O objetivo deste trabalho é a avaliação dos usos de água referentes à geração de energia hidroelétrica, navegação fluvial e abastecimento urbano de água, utilizou-se o Método dos Pesos e a Teoria dos Jogos (TJ) para subsidiar o tratamento multiobjetivo do problema. Para isso foram estabelecidos dois modelos com suporte da otimização via programação não linear, que contemplam as metodologias dos dois métodos mencionados. Os resultados obtidos por ambos os métodos foram próximos, sendo que o método dos pesos apresenta um menor grau de complexidade em sua estruturação, já a Teoria dos Jogos cooperativos, com embasamento em Harsanyi, se mostrou eficaz para o estudo e resultados coerentes com os métodos tradicionais. A TJ se mostrou mais eficiente em cenários com maior número de graus de liberdade e assim, indicada para situações onde é possível descumprir relaxar condições de contorno (restrições) em função de uma melhora global no resultado. Com a comparação dos resultados em cada caso, confirmou-se a viabilidade de aplicação de ambos os métodos como ferramenta de suporte à tomada de decisão em uma bacia hidrográfica, ressalta-se que a TJ tem solução ótima mais defensável em comparação com a programação multiobjetivo pois não precisa da atribuição de pesos aos objetivos. Assim confirma-se a tese de que a aplicação da TJ num problema de operação de reservatórios com múltiplos objetivos é tão eficiente quanto as aplicações tradicionais em que os "players" são diferentes agentes, mas todos concorrendo no mesmo objetivoAbstract: The reservoir operation involves many decision variables, which are chose to meet one or more objectives. A decision that has more than one objective can be established according to the preferences of the decision maker, but decisions of high complexity and impact are more defensible when they can be subsidized by mathematical models of decision support. The objective of this work is to evaluate the water uses related to the generation of hydroelectric power energy, river navigation and urban water supply. Using the Weights Method and Game Theory (GT) to support the multiobjective treatment of the problem. Two models were established with support of the optimization through nonlinear programming, which contemplate the methodologies of the two mentioned methods. The results by both methods were close, and the weights method presents a lower degree of complexity in its structuring, whereas the Cooperative Games Theory, based on Harsanyi, was effective for the study and results consistent with the methods traditional. The GT proved to be more efficient in scenarios with greater degrees of freedom and thus, indicated for situations where it is possible to relax boundary conditions (restrictions) due to an overall improvement in the result. With the comparison of the results in each case, the viability of applying both methods as a tool to support decision making in a watershed was confirmed, it is emphasized that the GT has an optimal solution that is more defensible in comparison with multiobjective programming because it does not need the attribution of weights to the objectives. This confirms the thesis that the application of GT in a problem of operation of reservoirs with multiple objectives is as efficient as the traditional applications in which the players are different agents, but all concurring in the same objectiveDoutoradoRecursos Hidricos, Energeticos e AmbientaisDoutor em Engenharia Civi

O impacto da aversão ao risco aplicada à solução de barganha de Kalai-Smorodinsky na negociação de contratos bilaterais no mercado de energia elétrica

Trabalho de Conclusão de Curso (graduação) — Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia de Produção, 2021.O processo histórico do mercado de eletricidade foi marcado no Brasil e fora dele, por uma presença cada vez mais forte da iniciativa privada e uma crescente desregulamentação, fato esse que proporcionou uma maior flexibilização e agilidade nas transações. Apesar dos benefícios desse modelo, os preços se tornaram mais voláteis e consequentemente o risco associado se tornou maior. Uma das formas de mitigar o risco intrínseco presente a este tipo de mercado é a negociação por volumes de energia, entregues em períodos específicos por meio de contratos bilaterais firmados entre uma Geradora e uma Distribuidora de energia elétrica. Tal estratégia diminui a volatilidade de preços e reduz a incerteza quanto à demanda. Diversos trabalhos têm por foco a proposição de soluções baseadas na Teoria dos Jogos e levando em consideração pontos de equilíbrio diferentes. É comum observar modelos propostos com base no ponto de equilíbrio de Nash ou de Kalai-Smorodinsky. Esse projeto avalia os impactos de medidas de aversão ao risco para Companhias Geradoras e Empresas Distribuidoras no Mercado Livre de Energia Elétrica aplicadas à Solução Barganha de Kalai-Smorodinsky (SBKS). A analise é realizada no sentido de verificar se diferentes medidas de aversão a risco podem impactar nos lucros esperados para cada participante e em seus pontos de equilíbrio, respectivamente.The historical process of the electricity market was marked in Brazil and abroad, by a stronger presence of the private sector and an increasingly deregulation, a fact that provided more flexibility and agility in transactions. Despite of the benefits of this model, prices become more volatile and, consequently, the associated risk was higher. One of the ways to mitigate the intrinsic risk present in this market is the negotiation of volumes of energy, delivered in specific periods through bilateral contracts instruments signed between a Generation Company (GC) and an Electricity Supplier Company (ESC). This strategy decreases price volatility and reduces uncertainty about demand. Several papers focus on proposing solutions based on Game Theory and considering different balance points. It is common to observe models proposed with Nash or Kalai- Smorodinsky equilibrium. This project assesses the impacts of risk aversion for GC and ESC in Free Electricity Markets using a Kalai-Smorodinsky Bargain Solution (SBKS). The analysis intend to evaluate if different risk aversion measures can impact the expected profits for each participant and their equilibrium points, respectively