Fabián Riquelme

Cooperation through social influence

We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this scenario by an influence game, a cooperative simple game in which a team (or coalition) of players succeeds if it is able to convince enough agents to participate in the task (to vote in favor of a decision). We take the linear threshold model as the influence model. We show first the expressiveness of influence games showing that they capture the class of simple games. Then we characterize the computational complexity of various problems on influence games, including measures (length and width), values (Shapley–Shubik and Banzhaf) and properties (of teams and players). Finally, we analyze those problems for some particular extremal cases, with respect to the propagation of influence, showing tighter complexity characterizations.

On the Complexity of the Decisive Problem in Simple and Weighted Games

Abstract We study the computational complexity of an important property of simple and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness can be decided for simple games in quasi-polynomial time, and for weighted games in polynomial time. The strongness condition poses the main difficulties. Instead, properness reduces the complexity of the problem. Specially if it is amplified by weightiness.

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.

Centrality measure in social networks based on linear threshold model

Abstract Centrality and influence spread are two of the most studied concepts in social network analysis. In recent years, centrality measures have attracted the attention of many researchers, generating a large and varied number of new studies about social network analysis and its applications. However, as far as we know, traditional models of influence spread have not yet been exhaustively used to define centrality measures according to the influence criteria. Most of the considered work in this topic is based on the independent cascade model. In this paper we explore the possibilities of the linear threshold model for the definition of centrality measures to be used on weighted and labeled social networks. We propose a new centrality measure to rank the users of the network, the Linear Threshold Rank (LTR), and a centralization measure to determine to what extent the entire network has a centralized structure, the Linear Threshold Centralization (LTC). We appraise the viability of the approach through several case studies. We consider four different social networks to compare our new measures with two centrality measures based on relevance criteria and another centrality measure based on the independent cascade model. Our results show that our measures are useful for ranking actors and networks in a distinguishable way.

Satisfaction and Power in Unanimous Majority Influence Decision Models

Abstract We consider decision models associated with cooperative influence games, the oblivious and the non-oblivious influence models. In those models the satisfaction and the power measures were introduced and studied. We analyze the computational complexity of those measures when the influence level is set to unanimity and the rule of decision is simple majority. We show that computing the satisfaction and the power measure in those systems are #P-hard.