Information Equilibrium Maximization Problem in Social Networks Based on Entropy

Personal cognition, product advertising and social recommendations are important factors to develop brand preferences, which directly influence consumer purchasing behaviors. A diversified brand preference landscape is conductive to preventing market monopolization, thus promoting healthier market competition. The entry of a new brand enhances market diversity and contributes to equilibrium of consumers' brand preferences. The new entrant stimulates competitive responses from incumbent brands because of catfish effect. Then market shares undergo redistribution as all brands increase their operational vitality in response to the competitive pressure. To select <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> users in a social network as advertisers of a new brand, this paper proposes the information equilibrium maximization (IEM) problem, and proves that the IEM is NP-hard, computing the objective function is #P-hard, and the objective function is neither modular nor monotonic. Then the entropy-based equilibrium degree maximization (EEDM) algorithm is proposed. In experiments, based on three methods of selecting seed nodes, E_qedm shows its superiority. It has strong robustness when the size of seedsets is large enough, and activation probability and update probability are more than 0.5. Besides, the number of initial preferences has little influence on the performance of E_qedm.