Abstract
An influence game is a simple game represented over an influence graph (i.e., a labeled, weighted graph) on which the influence spread phenomenon is exerted. Influence games allow applying different properties and parameters coming from cooperative game theory to the contexts of social network analysis, decision-systems, voting systems, and collective behavior. The exact calculation of several of these properties and parameters is computationally hard, even for a small number of players. Two examples of these parameters are the length and the width of a game. The length of a game is the size of its smaller winning coalition, while the width of a game is the size of its larger losing coalition. Both parameters are relevant to know the levels of difficulty in reaching agreements in collective decision-making systems. Despite the above, new bio-inspired metaheuristic algorithms have recently been developed to solve the NP-hard influence maximization problem in an efficient and approximate way, being able to find small winning coalitions that maximize the influence spread within an influence graph. In this article, we apply some variations of this solution to find extreme winning and losing coalitions, and thus efficient approximate solutions for the length and the width of influence games. As a case study, we consider two real social networks, one formed by the 58 members of the European Union Council under nice voting rules, and the other formed by the 705 members of the European Parliament, connected by political affinity. Results are promising and show that it is feasible to generate approximate solutions for the length and width parameters of influence games, in reduced solving time.
Highlights
Cooperative game theory deals with the study of players forming coalitions to achieve a common benefit, enforcing cooperative behavior [1]
Besides the traditional forms of representation of simple games [6], since the 2010s, different formulations based on graphs have emerged, with the aim of applying the knowledge acquired in cooperative game theory in network science [7]
The results obtained for computing the length and the width in the case study of the network of European parliamentarians related by political affinity are presented and discussed below
Summary
Cooperative game theory deals with the study of players forming coalitions to achieve a common benefit, enforcing cooperative behavior [1]. Besides the traditional forms of representation of simple games [6], since the 2010s, different formulations based on graphs have emerged, with the aim of applying the knowledge acquired in cooperative game theory in network science [7]. In this context, influence games arise as simple games defined by influence graphs (i.e., weighted, labeled graphs) on which an influence spread phenomenon is exerted. Influence games and influence graphs have been already used to solve problems of multi-agent systems [8], social network analysis [9,10], and collective decision-making models [11,12]
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