En este trabajo realizamos una propuesta de asignación de las diputaciones federales por representación proporcional en el proceso electoral de 2021 en México utilizando el índice de representación absoluta para medir la distancia entre la asignación y el total de votos obtenidos por los partidos. Y planteamos un procedimiento que asigna diputados plurinominales en cada circunscripción federal en partidos no sobrerrepresentados. Con ello obtenemos una mejor manera de conformar la Cámara de Diputados bajo este índice con un menor número de diputados plurinominales, cambiando la forma de asignación en las circunscripciones.

The Myerson value is a characterized allocation rule for analyzing games with a coalitional structure, merging ideas from graph theory and classical cooperative game theory. In this article, we extend these ideas to characterize a solution for cooperative interval games, which consist of a finite set of players, where the coalition values are compact intervals of real numbers. We adapt the axiom of efficiency by connected components, which Myerson proposed in the classical theory of cooperative games with graphs, to interval games. Additionally, we introduce the concept of superadditivity under tau and define a new axiom, which we call equity with respect to tau. With these two properties, we propose a new characterization of the interval Myerson value.

This paper explores a different approach to supply chain modeling through the game theory perspective. Particularly, we explain a two-echelon one single chan-nel supply chain under common assumptions through a signaling game with the classical structure. In our first approach, we prove that there are many different ways to obtain an equilibrium, but too many of these strategies do not necessarily imply cooperative behavior between agents. Later, we propose some modifications to the original assumptions which let us obtain a unique equilibrium that ensures a cooperative behavior between agents.

En este artículo exploramos un enfoque diferente para el modelado de una cadena de suministro desde la perspectiva de la teoría de juegos. En particular, explicamos una cadena de suministro de dos escalones y un solo canal bajo supuestos comunes a través de un juego de señales con la estructura clásica. Probamos que, en nuestro primer enfoque, existen varias maneras racionales de actuar que conducen a los agentes a equilibrios del juego, sin embargo, la mayoría de estas estrategias no implican necesariamente un comportamiento de cooperación entre los agentes. Posteriormente, proponemos algunas modificaciones a los supuestos originales que nos permiten obtener un equilibrio único que además garantiza la cooperación entre los agentes favoreciendo la calidad en el intercambio de información

This article shows a Symmetrical Bayesian Nash Equilibrium in a context of m simultaneous first-price sealed-bid auctions and n bidders for complementary goods. We consider that the individual valuations of the m goods are common knowledge and identical among bidders and if the whole set of goods is gained, a private independent extra profit is obtained by the winner. For relaxing and solving the so-many mathematical complications involved in the general case we followed a classical methodology and proposed a particular bidding function that implies linear separability. Under this assumptions we obtain a Symmetric Bayesian Nash Equilibrium which functional form implies the classic quasi-linear property for bivariate functions. On addition, we compare the seller expected revenue between auctioning the complete set in one single first-price sealed-bid auction versus auctioning each item in m simultaneous first-price sealed-bid auctions.

Objetivo: Estudiar, desde el punto de vista del vendedor, la manera de subastar un conjunto finito de bienes idénticos donde se otorga un cierto premio al postor que obtenga el conjunto completo de bienes, tomando en cuenta el comportamiento estratégico de los postores. Metodología: Se modela la situación como un juego bayesiano considerando el espacio de estrategias de cada jugador como R+m. Resultados: Se muestra un equilibrio bayesiano simétrico y se demuestra que el vendedor es indiferente entre algunas maneras de ofrecer la utilidad extra, al obtener el mismo rendimiento esperado. Limitaciones: El modelo soló considera el caso de bienes idénticos. Originalidad: Se encuentra la puja de equilibrio para un caso de m subastas simultáneas y n postores, bajo el mecanismo del primer precio considerando utilidad extra modeladas mediante juegos bayesianos. Conclusiones: Los cambios en el rendimiento esperado del vendedor no son sensibles ante algunas maneras de otorgar el incentivo.

In this paper we show several results regarding to the classical cost sharing problem when each agent requires a set of services but they can share the benefits of one unit of each service, i.e. there is non rival consumption. Specifically, we show a characterized solution for this problem, mainly adapting the well-known axioms that characterize the Shapley value for TU-games into our context. Finally, we present some additional properties that the shown solution satisfy.

In this paper we study TU-games where the cooperation structure among the players is modeled by a forest. Using the classical component efficiency axiom and a generalized version of the component fairness axiom we obtain a family of solutions. We show that every solution in this family isbased on a process of transfers among the players, and the average tree solution belongs to the family. Finally, we obtain a solution based on the degree of the nodes and we study a set of properties satisfied by this family.

In this paper we propose an algorithm for solving a fair division problem: We want to find a distribution of a set of divisible items among a set of agents such that the agent who is getting the lowest amount obtains his maximum possible value. Even more, according to the found distribution, each agent obtains the same amount, and this is as high as possible. We model this situation as a linear programming problem and we use its dual problem for solving it. For doing this, we associate a bipartite graph with each set of dual variables. The algorithm presented uses the intrinsic relations in this kind of graphs for searching the optimal solution for the primal and dual problems. Finally, we show the convergence of the proposed algorithm.

A well-known result related to bankruptcy problems establishes that a vector is a bankruptcy allocation if and only if it belongs to the core of the associated O’Neill’s bankruptcy game. In this paper we show that this game is precisely the unique TU-game based on convex functions that satisfies the previous result. In addition, given a bankruptcy problem, we show a way for constructing bankruptcy games such that the set of bankruptcy allocations is a subset of their core or their core is a subset of the set of bankruptcy allocations. Also, we show how these results can be applied for finding new bankruptcy solutions.

In this paper we characterize a solution for a discrete cost sharing problem where each agent requires a set of services but they can share them with each other, Also, the services provider can offer any subset of services. So, the agents have to distribute the cost of using the whole set of services amongst them. In our proposed solution, we work with the cost function as a cooperative game. and the Shapley value of this game is regarded as the price by each service, Then, we divide equally the service price among the agents who consume it, In addition, we show some properties that our solution satisfies,

In this paper we introduce a new class of cooperative games. We define a characteristic function over the cycles of a digraph. We present a mathematical model for this situation and an axiomatic characterization of a solution for this class of cooperative games. This is introduced as a method to measure the importance of the nodes in a digraph, and can be related with the Shapley value of a game in characteristic function form. Also, we extend the modeling by applying coalitional structures for the nodes and r-efficient solutions, where the allocation amount is a real number r, showing axiomatic solutions in both cases.

In this paper we study the discrete cost sharing problem. We restrict the problem when there exists only a pair of agents with the same demand of discrete goods (not necessarily the same kind of goods). We create a non-cooperative game based on solutions defined by paths and then, we show a solution for the cost sharing problem that is a Nash equilibrium for our non-cooperative situation. Also, we show some properties of the proposed solution.