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

This paper considers trial-offer markets where consumer preferences are modeled by a multi-nomial logit with social influence and position bias. The social signal for a product is givenby its current market share raised to power r (or, equivalently, the number of purchases raisedto the power of r). The paper shows that, when r is strictly between 0 and 1, and a staticposition assignment (e.g., a quality ranking) is used, the market converges to a unique equi-librium where the market shares depend only on product quality, not their initial appeals orthe early dynamics. When r is greater than 1, the market becomes unpredictable. In manycases, the market goes to a monopoly for some product: Which product becomes a monopolydepends on the initial conditions of the market. These theoretical results are complemented byan agent-based simulation which indicates that convergence is fast when r is between 0 and 1,and that the quality ranking dominates the well-known popularity ranking in terms of marketefficiency. These results shed a new light on the role of social influence which is often blamedfor unpredictability, inequalities, and inefficiencies in markets. In contrast, this paper showsthat, with a proper social signal and position assignment for the products, the market becomespredictable, and inequalities and inefficiencies can be controlled appropriately.