Popularity signals in trial-offer markets with social influence and position bias

This paper considers trial-offer and freemium markets where consumer preferences are modeled by a multinomial logic model with social influence and position bias. The social signal for a product i is its market share raised to some power r. The paper shows that, when 0 1, the market become unpredictable and goes most likely to a monopoly for some product. Which product becomes a monopoly depends on the initial conditions of the market. These theoretical results are complemented by an agent-based simulation which indicates that convergence is fast when 0 < r < 1 and that the quality ranking dominates the well-known popularity ranking in terms of market efficiency. These results shed a new light on the role of social influence which has been believed to produce unpredictability, inequalities, and inefficiencies in markets. In contrast, this paper shows that, with a proper social signal and a proper position assignment for the products, the market becomes predictable and inequalities and inefficiencies can be controlled.