Influence network design via multi-level optimization considering boundedly rational user behaviours in social media networks

Abstract

Social media networks have been playing an increasingly more important role for both socialization and information diffusion. Political campaign can gain more supporters by attracting more mass attention and influencing them directly, while commercial campaigns can increase their companies’ profits by expanding social media connection with new users. To build the optimal network structure to influence the whole, this paper studies mathematical models to simulate the users’ behaviours interacting with others in the information provider’s network. The behaviours of concerns include information re-posting and following/unfollowing other users. Linear threshold propagation model is used to determine the re-posting actions, Boundedly Rational User Equilibrium (BRUE) models are used to determine the following or unfollowing actions. Hence, the topology of the network changes and depends on the information provider’s plan to post various kinds of information. A three-level optimization model is proposed to maximize total number of connections, the goal of the top level. The second level simulates user behaviours under BRUE. The third level maximizes the each user’s utility defined in the second level. This paper solves this problem using exact algorithms for a small-scale synthetic network. For a large-scale problem, this paper uses heuristic algorithms based on large neighbourhood search. This paper also discusses possible reasons why the BRUE model may be a more accurate simulation of users’ actions compared to game theory. Comparisons from the BRUE model to game theoretical model show that the BRUE model performs significantly better than game theoretical model.