  This paper considers trial-offer markets where consumer preferences are
modeled by a multinomial logit with social influence and position bias. The
social signal for a product is given by its current market share raised to
power r (or equivalently the number of purchases raised to the power of r). The
paper shows that, when r is strictly between 0 and 1, and a static position
assignment (e.g., a quality ranking) is used, the market converges to a unique
equilibrium where the market shares depend only on product quality, not their
initial appeals or the early dynamics. When r is greater than 1, the market
becomes unpredictable. In many cases, the market goes 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 r is between 0 and 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 is often blamed for unpredictability, inequalities, and
inefficiencies in markets. In contrast, this paper shows that, with a proper
social signal and position assignment for the products, the market becomes
predictable, and inequalities and inefficiencies can be controlled
appropriately.
