Natividad Llorca

Game Theory Techniques for University Management: An Extended Bankruptcy Model

In this paper we analyze a conflict situation in university management. This situation deals with how to allocate money among faculties to buy equipment for teaching laboratories. We will tackle this real problem using tools from Game Theory. We discuss the proposal which has been implemented in the Miguel Hernández University. Related to this kind of situation we introduce an extended bankruptcy problem, in which two ways of measuring the demands of the administrative entities exist: the “objective entitlements” and the “claims”. We study and propose suitable bankruptcy rules for this new type of problem.

Semi-Infinite Assignment Problems and Related Games

Abstract. In this paper we look at semi-infinite assignment problems. These are situations where a finite set of agents of one type has to be assigned to an infinite set of agents of another type. This has to be done in such a way that the total profit arising from these assignments is as large as possible. An infinite programming problem and its dual arise here, which we tackle with the aid of finite approximations. We prove that there is no duality gap and we show that the core of the corresponding game is nonempty. Finally, the existence of optimal assignments is discussed.

An Integrated Transport System for Alacant's Students. UNIVERCITY

The dispersion between the different university campuses in Alacant raises the social necessity of designing a transport system capable of efficiently connecting the villages and cities of Alacant with the campuses. In this paper, we develop a centralized transport system for university students in the province of Alacant.

A cost allocation rule for k-hop minimum cost spanning tree problems

In this note, we prove that the core of a k-hop minimum cost spanning tree problem could be empty. We also introduce a cost sharing rule based on bankruptcy problems. We prove that this rule satisfies meaningful properties for these problems.

The Owen set and the core of semi-infinite linear production situations

We study linear production situations with an infinite number of production techniques. Such a situation gives rise to a semi-infinite linear program. Related to this program, we introduce primal and dual games and study relations between these games, the cores of these games and the so-called Owen set.

How to divide a cake when people have different metabolism

This paper deals with bankruptcy problems in which the players have different utility functions defined in terms of the quantity of allocated resources. We tackle this kind of situation by means of a game without transferable utility and provide two characterizations of the CEA-rule in this context.

The core and related solution concepts for infinite assignment games

Assignment problems where both sets of agents that have to be matched are countably infinite, the so-called infinite assignment problems, are studied as well as the related cooperative assignment games. Further, several solution concepts for these assignment games are studied. The first one is the utopia payoff for games with an infinite value. In this solution each player receives the maximal amount he can think of with respect to the underlying assignment problem. This solution is contained in the core of the game.Second, we study two solutions for assignment games with a finite value. Our main result is the existence of core-elements of these games, although they are hard to calculate. Therefore another solution, the f-strong ε-core is studied. This particular solution takes into account that due to organisational limitations it seems reasonable that only finite groups of agents will eventually protest against unfair proposals of profit distributions. The f-strong ε-core is shown to be nonempty.

On the Owen Set of Transportation Solutions

This paper presents an axiomatic characterization of the Owen set of transportation games. In the characterization we use six properties including consistency (CONS2) and splitting and merging (SM) which are firstly proposed and defined for this setup in the present paper.

Equilibria in a competitive model arising from linear production situations with a common-pool resource

In this paper we deal with linear production situations in which there is a limited common-pool resource, managed by an external agent. The profit that a producer can attain depends on the amount of common-pool resource obtained through a certain procedure. We contemplate a competitive process among the producers and study the corresponding non-cooperative games, describing their (strict) Nash equilibria in pure strategies. It is shown that strict Nash equilibria form a subset of strong Nash equilibria, which in turn form a proper subset of Nash equilibria.

A new rule for source connection problems

In this paper we study situations where a group of agents require a service that can only be provided from a source, the so-called source connection problems. These problems contain the standard fixed tree, the classical minimum spanning tree and some other related problems such as the k-hop, the degree constrained and the generalized minimum spanning tree problems among others. Our goal is to divide the cost of a network among the agents. To this end, we introduce a rule which will be referred to as a painting rule because it can be interpreted by means of a story about painting. Some meaningful properties in this context and a characterization of the rule are provided.