Essays on Cooperative Games with Restricted Cooperation and Simple Games

In this dissertation we propose and characterize new values for cooperative games with restricted cooperation and simple games. In each of the studied models parallel characterizations of different values are proposed to ease the comparison among them

Alineamiento docente y aprendizaje basado en tareas. Una experiencia para mejorar la motivación del alumnado

En este trabajo presentamos una primera experiencia dirigida a mejorar la motivación del alumnado de la asignatura Matemáticas I. La idea fundamental consiste en aprovechar la motivación extrínseca por aprobar la asignatura para potenciar el aprendizaje basado en problemas. Para ello, se ha modificado el sistema de evaluación continuada de la asignatura dando más peso a las sesiones prácticas. La valoración de la experiencia ha sido positiva aunque entendemos que hay mucho margen de mejora

Games with Graph Restricted Communication and Levels Structure of Cooperation

We analyze surplus allocation problems where cooperation between agents is restricted both by a communication graph and by a sequence of embedded partitions of the agent set. For this type of problem, we define and characterize two new vàlues extending the Shapley value and the Banzhaf value respectively. Our results enable the axiomatic comparison between the two values and provide some basic insights for the analysis of fair resource allocation in nowadays fully integrated societies

On the added value of quad-pol data in a multi-temporal crop classification framework based on RADARSAT-2 imagery

Polarimetric SAR images are a rich data source for crop mapping. However, quad-pol sensors have some limitations due to their complexity, increased data rate, and reduced coverage and revisit time. The main objective of this study was to evaluate the added value of quad-pol data in a multi-temporal crop classification framework based on SAR imagery. With this aim, three RADARSAT-2 scenes were acquired between May and June 2010. Once we analyzed the separability and the descriptive analysis of the features, an object-based supervised classification was performed using the Random Forests classification algorithm. Classification results obtained with dual-pol (VV-VH) data as input were compared to those using quad-pol data in different polarization bases (linear H-V, circular, and linear 45º), and also to configurations where several polarimetric features (Pauli and Cloude–Pottier decomposition features and co-pol coherence and phase difference) were added. Dual-pol data obtained satisfactory results, equal to those obtained with quad-pol data (in H-V basis) in terms of overall accuracy (0.79) and Kappa values (0.69). Quad-pol data in circular and linear 45º bases resulted in lower accuracies. The inclusion of polarimetric features, particularly co-pol coherence and phase difference, resulted in enhanced classification accuracies with an overall accuracy of 0.86 and Kappa of 0.79 in the best case, when all the polarimetric features were added. Improvements were also observed in the identification of some particular crops, but major crops like cereals, rapeseed, and sunflower already achieved a satisfactory accuracy with the VV-VH dual-pol configuration and obtained only minor improvements. Therefore, it can be concluded that C-band VV-VH dual-pol data is almost ready to be used operationally for crop mapping as long as at least three acquisitions in dates reflecting key growth stages representing typical phenology differences of the present crops are available. In the near future, issues regarding the classification of crops with small field sizes and heterogeneous cover (i.e., fallow and grasslands) need to be tackled to make this application fully operational

Parallel characterizations of a generalized shapley value and a generalized banzhaf value for cooperative games with level structure of cooperation

We present parallel characterizations of two different values in the framework of restricted cooperation games. The restrictions are introduced as a finite sequence of partitions defined on the player set, each of them being coarser than the previous one, hence forming a structure of different levels of a priori unions. On the one hand, we consider a value first introduced in Ref. [18], which extends the Shapley value to games with different levels of a priori unions. On the other hand, we introduce another solution for the same type of games, which extends the Banzhaf value in the same manner. We characterize these two values using logically comparable properties

Vertical syndication-proof competitive prices in multilateral assignment markets

We consider a market comprising a number of perfectly complementary and homogeneous commodities. We concentrate on the incentives for firms producing these commodities to merge and form a vertical syndicate. The main result establishes that the nucleolus of the associated market game corresponds to the unique vector of prices with the following properties: (i) they are vertical syndication-proof, (ii) they are competitive, (iii) they yield the average of the buyers- and the sellers-optimal allocations in bilateral markets, and (iv) they depend on the traders' bargaining power but not on their identity. The proof uses an isomorphism between our class of market games and the entire class of bankruptcy games

Externalities and the (Pre)nucleolus in Cooperative Games

In most economic applications of cooperative games, externalities prevail: the worth of a coalition depends on how the other players are organized. We show that there is a unique natural way of extending the prenucleolus to games with coalitional externalities. This is in contrast to the Shapley value and the core for which many different extensions have been proposed

The a-serial cost sharing rule

A new family of cost sharing rules for cost sharing problems is proposed. This family generalizes the family of α-serial cost sharing rules (Albizuri in Math Soc Sci 60:24–29, 2010) which contains the serial cost sharing rule (Moulin and Shenker in Econometrica 60:1009 – 1037, 1992) among others. Every rule of the family is characterized by means of two properties

Graphs and (levels of) cooperation in games: Two ways how to allocate the surplus

We analyze surplus allocation problems where cooperation between agents is restricted both by a communication graph and by a sequence of embedded partitions of the agent set. For this type of problem, we define and characterize two new values extending the Shapley value and the Banzhaf value, respectively. Our results enable the axiomatic comparison between the two values and provide some basic insights for the analysis of fair resource allocation in today's fully integrated societies

Power distribution in the Basque Parliament using games with externalities

In this paper we study the distribution of power in the Basque Parliament since the restoration of the Spanish democracy. The classic simple games do not fit with the particular voting rule that it is used to invest the president of the regional government. In order to model this voting mechanism we incorporate coalitional externalities to the game. We use the extensions of the most popular power indices to games with externalities that have been proposed in the most recent literature. Moreover, we propose a method to estimate the probability of a given coalition based on the ideological positions of its members in a two-dimensional political spectrum