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

Abstract

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.

Blockbuster or Niche? Competitive Strategy Under Network Effects

“…1 n } cannot reach the boundary of S in an arbitrarily finite time. The convergence of the flowx(t) has been proved according to the proof of Theorem 6.2 in Maldonado et al (2015) and hence the proof of part (i) is complete.…”

“…From a methodological point of view, our framework has various similarities with Maldonado et al (2015). In their framework, customer choices are captured by a discrete choice model in which product utilities depend on the song's quality, position bias, and a social influence signal representing past purchases.…”

“…Based on their framework, we further characterize the case of r ≥ 1 analytically by obtaining the probability that each product goes to a monopoly when r ≥ 1 and showing that the product variety would expand when r increases from 1 to infinity. Maldonado et al (2015) focus on the position assignment that ranks the products in cultural markets with social influence. Unlike their paper, our work focuses on the product variety in an industry with network effect and on unifying the long tail theory and blockbuster phenomenon in one model.…”

Opinion formation and targeting when persuaders have extreme and centrist opinions

“…The competition between firms aiming at maximizing product adoption by consumers located in a social network is also studied in [13], [26], and [41]. While social influence is often blamed for unpredictability, inequalities and inefficiencies in markets, [53] show that with a proper social signal and position assignment for the products, the market can become predictable, and inequalities and inefficiencies can be controlled. [35] propose a framework to study optimal interventions, when individuals interact strategically with their neighbors.…”

Reviews and Self-Selection Bias with Operational Implications

“…Some recent papers in the Operations Management literature model the dynamics of learning from reviews and study analytically the learning outcome and the firm's optimal decisions. Maldonado et al (2018) study rating dynamics when customers choose according to a Multinomial 7 LH(08) HPZ( 17) AMMO( 18) BS( 18) VMS(18) Our Paper Acquisition Bias X X X X X Under-reporting Bias X X Bounded Rationality X X X X X Rational Bayesian Update X X Asymptotics X X X X Multiple Products X X Firm's Pricing and Assortment Decision X…”