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.

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We study a trial-offer market where consumers may purchase one of two competing products. Consumer preferences are affected by the products quality, their appeal, and their popularity. While the asymptotic convergence or stationary states of these, and related dynamical systems, has been vastly studied, the literature regarding the transitory dynamics remains surprisingly sparse. To fill this gap, we derive a system of Ordinary Differential Equations, which is solved exactly to gain insight into the roles played by product qualities and appeals in the market behavior. We observe a logarithmic tradeoff between quality and appeal for medium and long-term marketing strategies: The expected market shares remain constant if a decrease in quality is followed by an exponential increase in the product appeal. However, for short time horizons, the trade-off is linear. Finally, we study the variability of the dynamics through Monte Carlo simulations and discover that low appeals may result in high levels of variability. The model results suggest effective marketing strategies for short and long time horizons and emphasize the significance of advertising early in the market life to increase sales and predictability.

Social influence is ubiquitous in cultural markets, from book recommendations in Amazon, to song popularities in iTunes and the ranking of newspaper articles in the online edition of the New York Times to mention only a few. Yet social influence is often presented in a bad light, often because it supposedly increases market unpredictability.Here we study a model of trial-offer markets, in which participants try products and later decide whether to purchase. We consider a simple policy which ranks the products by quality when presenting them to market participants. We show that, in this setting, market efficiency always benefits from social influence. Moreover, we prove that the market converges almost surely to a monopoly for the product of highest quality, making the market both predictable and asymptotically optimal. Computational experiments confirm that the quality ranking policy identifies "blockbusters" in reasonable time, outperforms other policies, and is highly predictable.These results indicate that social influence does not necessarily increase market unpredictability. The outcome really depends on how social influence is used.

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