Papers by Julio Rodrigo Fernández García
Symmetry
A cooperative game represents a situation in which a set of agents form coalitions in order to ac... more A cooperative game represents a situation in which a set of agents form coalitions in order to achieve a common good. To allocate the benefits of the result of this cooperation there exist several values such as the Shapley value or the Banzhaf value. Sometimes it is considered that not all communications between players are feasible and a graph is introduced to represent them. Myerson (1977) introduced a Shapley-type value for these situations. Another model for cooperative games is the Owen model, Owen (1977), in which players that have similar interests form a priori unions that bargain as a block in order to get a fair payoff. The model of cooperation introduced in this paper combines these two models following Casajus (2007). The situation consists of a communication graph where a two-step value is defined. In the first step a negotiation among the connected components is made and in the second one players inside each connected component bargain. This model can be extended to f...
International Journal of General Systems
A cooperative game for a set of agents establishes a fair allocation of the profit obtained for t... more A cooperative game for a set of agents establishes a fair allocation of the profit obtained for their cooperation. In order to obtain this allocation, a characteristic function is known. It establishes the profit of each coalition of agents if this coalition decides to act alone. Originally players are considered symmetric and then the allocation only depends on the characteristic function; this paper is about cooperative games with an asymmetric set of agents. We introduced cooperative games with a soft set of agents which explains those parameters determining the asymmetry among them in the cooperation. Now the characteristic function is defined not over the coalitions but over the soft coalitions, namely the profit depends not only on the formed coalition but also on the attributes considered for the players in the coalition. The best known of the allocation rules for cooperative games is the Shapley value. We propose a Shapley kind solution for soft games.
Fuzzy Sets and Systems
Abstract A cooperative game for a set of agents establishes a fair allocation of the profit obtai... more Abstract A cooperative game for a set of agents establishes a fair allocation of the profit obtained for their cooperation. The best known of these allocations is the Shapley value. A communication structure defines the feasible bilateral communication relationships among the agents in a cooperative situation. Some solutions incorporating this information have been defined from the Shapley value: the Myerson value, the position value, etc. Later fuzzy communication structures were introduced. In a fuzzy communication structure the membership of the players and the relations among them are leveled. Several ways of defining the Myerson value for games on fuzzy communication structure were proposed, one of them is the Choquet by graphs (cg) version. Now we study in this work the cg-position value and its calculation. The cg-position value is defined as a solution for games with fuzzy communication structure which considers the bilateral communications as players. So, the Shapley value is applied for a new game (the link game) over the fuzzy sets of links in the fuzzy communication structure and the profit obtained for each link is allocated between both players in the link. As we see in our examples and results the cg-position value is more concerned with the graphical position of the players and their communications than the other cg-values. In this paper we also introduce a procedure to compute exactly the position value, avoiding to calculate the characteristic function of the link game for all coalitions. This procedure is used to determine the cg-position value. Finally we compare the new value with other cg-values in an applied example about the power of the groups in the European Parliament.
International Journal of Approximate Reasoning
The Banzhaf index is a function determining the power or influence in the decision of a set of ag... more The Banzhaf index is a function determining the power or influence in the decision of a set of agents. The extension of this index to the family of the cooperative games is named Banzhaf value. The relationships of closeness among the agents should modify their power. Games with a priori unions study situations where the closeness relations among the agents are taken into account. In this model the agents are organized in an a priori partition where each element of the partition represents a group of agents with close interests or ideas. The power is determined in two steps, first as a problem among the unions and later, inside each one, the power of each agent is determined. Proximity relations extend this model considering leveled closeness among the agents. In this paper we analyze a version of the Banzhaf value for games with a proximity relation and we show the interest of this value by applying it to the allocation of the power of the political groups in the European Parliament.
European Journal of Operational Research, 2015
A cooperative game consists of a set of players and a characteristic function determining the max... more A cooperative game consists of a set of players and a characteristic function determining the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate, regardless of the actions that the other players take. The relationships of closeness among the players should modify the bargaining among them and therefore their payoffs. The first models that have studied this closeness used a priori unions or undirected graphs. In the a priori union model a partition of the big coalition is supposed. Each element of the partition represents a group of players with the same interests. The groups negotiate among them to form the grand coalition and later, inside each one, players bargain among them. Now we propose to use proximity relations to represent leveled closeness of the interests among the players and extending the a priori unions model.
Mathematical Social Sciences, 2003
International Journal of Game Theory, 2007
Fuzzy Sets and Systems, 2013
Fuzzy Sets and Systems, 2013
… Working Papers at …, 2004
Downloadable! The present paper develops some general conditions under which we analize the bicoo... more Downloadable! The present paper develops some general conditions under which we analize the bicooperative games introduced by Bilbao (2000). We define the probabilistic values for these games and observe in detail the axioms that characterize such values. Following the ...
and centrA: RESUMEN El objetivo de este trabajo es analizar un concepto de solución que asigna a ... more and centrA: RESUMEN El objetivo de este trabajo es analizar un concepto de solución que asigna a cada juego bicooperativo un único vector. En el contexto de los juegos bicooperativos introducidos por Bilbao (2000), definimos una solución denominada valor de Shapley porque este valor puede interpretarse de una ma nera semejante al clásico valor de Shapley para juegos cooperativos. El resultado más importante del trabajo es una caracterización axiomática de este valor.
Annals of Operations Research, 2002
The complexity of a computational problem is the order of computational resources which are neces... more The complexity of a computational problem is the order of computational resources which are necessary and sufficient to solve the problem. The algorithm complexity is the cost of a particular algorithm. We say that a problem has polynomial complexity if its computational complexity is a polynomial in the measure of input size. We introduce polynomial time algorithms based in generating functions for computing the Myerson value in weighted voting games restricted by a tree. Moreover, we apply the new generating algorithm for computing the Myerson value in the Council of Ministers of the European Union restricted by a communication structure.
European Journal of …, 2002
In this paper we analyze ternary bicooperative games, which are a refinement of the concept of a ... more In this paper we analyze ternary bicooperative games, which are a refinement of the concept of a ternary voting game introduced by Felsenthal and Machover. Furthermore, majority voting rules based on the difference of votes are simple bicooperative games. First, we define the concepts of the defender and detractor swings for a player. Next, we introduce the Banzhaf power index and the normalized Banzhaf power index. The main result of the paper is an axiomatization of the Banzhaf power index for the class of ternary bicooperative games. Moreover, we study ternary bicooperative games with two lists of weights and compute the Banzhaf power index using generating functions.
European Journal of Operational Research, 2009
European Journal of Operational Research, 2007
The aim of this paper is to analyze the distribution of voting power in the Constitution for the ... more The aim of this paper is to analyze the distribution of voting power in the Constitution for the enlarged European Union. By using generating functions, we calculate the Banzhaf power indices for the European countries in the Council of Ministers under the decision rules prescribed by the Treaty of Nice and the new rules proposed by the European Constitution Treaty. Moreover, we analyze the power of the European citizens under the egalitarian model proposed by Felsenthal and Machover [D.S. Felsenthal, M. Machover, The measurement of voting power: Theory and practice, problems and paradoxes, Edward Elgar, Cheltenham, 1998].
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Papers by Julio Rodrigo Fernández García