Network topology design to influence the effects of manipulative behaviors in a social choice procedure

A social choice procedure is modeled as a Nash game among the social agents. The agents are communicating with each other through a social communication network modeled by an undirected graph and their opinions follow a dynamic rule modelling conformity. The agents’ criteria for this game are describing a trade off between self-consistent and manipulative behaviors. Their best response strategies are resulting in a dynamic rule for their actions. The stability properties of these dynamics are studied. In the case of instability, which arises when the agents are highly manipulative, the stabilization of these dynamics through the design of the network topology is formulated as a constrained integer programming problem. The constraints have the form of a Bilinear Matrix Inequality (BMI), which is known to result in a nonconvex feasible set in the general case. To deal with this problem a Genetic Algorithm, which uses an LMI solver during the selection procedure, is designed. Finally, through simulations we observe that in the case of topologies with few edges, e.g. a star or a ring, the isolation of the manipulative agents is an optimal (or suboptimal) design, while in the case of well-connected topologies the addition or the rewiring of just a few links can diminish the negative effects of manipulative behaviors.