7 research outputs found
On the complexity of exchanging
We analyze the computational complexity of the problem of deciding
whether, for a given simple game, there exists the possibility of rearranging the participants in a set of j given losing coalitions into a set of j winning coalitions. We also look at the problem of turning winning coalitions into losing coalitions. We analyze the problem when the simple game is represented by a list of wining, losing, minimal winning or maximal loosing coalitions.Peer ReviewedPostprint (author’s final draft
Dimension and codimension of simple games
This paper studies the complexity of computing a representation of a simple
game as the intersection (union) of weighted majority games, as well as, the
dimension or the codimension. We also present some examples with linear
dimension and exponential codimension with respect to the number of players.Comment: 5 page
Combinatorial structures to modeling simple games and applications
We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-)heuristics algorithms and parallel programming, among others.Peer ReviewedPostprint (published version
Combinatorial structures to construct simple games and molecules
We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-) heuristics algorithms and parallel programming, among others.Peer ReviewedPostprint (published version
Publicacions cientÃfiques de l'Escola Politècnica Superior d'Enginyeria de Manresa (EPSEM) curs 2015-2016
Aquest informe ha estat elaborat per la Biblioteca del Campus Universitari de Manresa per proveir de dades la memòria del curs2015-2016. Recull les publicacions del personal docent i investigador del Centre, obtingudes de Futur.upc.edu i analitzades amb Scopus.Postprint (published version
Forms of representation for simple games: sizes, conversions and equivalences
Simple games are cooperative games in which the benefit that a coalition may have is always binary, i.e., a coalition may either win or loose. This paper surveys different forms of representation of simple games, and those for some of their subfamilies like regular games and weighted games. We analyze the forms of representations that have been proposed in the literature based on different data structures for sets of sets. We provide bounds on the computational resources needed to transform a game from one form of representation to another one. This includes the study of the problem of enumerating the fundamental families of coalitions of a simple game. In particular we prove that several changes of representation that require exponential time can be solved with polynomial-delay and highlight some open problems.Peer ReviewedPostprint (author’s final draft
On the complexity of exchanging
We analyze the computational complexity of the problem of deciding
whether, for a given simple game, there exists the possibility of rearranging the participants in a set of j given losing coalitions into a set of j winning coalitions. We also look at the problem of turning winning coalitions into losing coalitions. We analyze the problem when the simple game is represented by a list of wining, losing, minimal winning or maximal loosing coalitions.Peer Reviewe