Distributed Evolutionary Games Reaching Power Indexes: Navigability in a Social Network of Smart Objects

In the context of coalitional games, a power index allows to determine the magnitude of contributions associated to each player, i.e., a power index provides information about how influential or relevant a player is in a cooperative interaction. Nevertheless, if the number of involved players is big, then the computation of a power index might become intractable. In this paper, we show how to construct a fullpotential game whose Nash equilibrium coincides with the Shapley or Banzhaf power index for a family of characteristic functions. Therefore, distributed non-cooperative algorithms can be used for cooperative-game purposes. As a consequence, both the computational time and the information requirements are reduced, allowing the use of power indexes in large-scale systems. As an illustrative example, we present a large-scale social network of smart objects where it is desired to enhance the navigability by means of local decisions.