Individual Rationality and Social Efficiency in an Information Contagion Model

In the Arthur-Lane information contagion model, agents choose sequentially between two competing products, basing their decisions upon information obtained from a sample of previous adopters. The market shares that each product obtains depend upon the true difference in performance between the products, but also on the number of previous adopters each agent samples and the way in which agents use the sample information to guide their product choice. If an agent in the information contagion world were to consult a statistician, he would surely be advised to sample more previous adopters rather than less (assuming observations are costless) and to base his decision rule on the value of sufficient statistics for the products’s unobservable performance characteristics. Bayesian statisticians might also recommend that the agent choose the product that maximizes his expected utility. Surprisingly, these recommendations can lead to undesirable effects at the social level. First, giving individual agents access to more information can lead to smaller market share for the superior product. Second, a simple rule-of-thumb based on insufficient statistics always leads to an asymptotic market share of 100% for the better product. No rule based on sufficient statistics enjoys this property. In particular, Bayesian optimization can result in substantial market share for the inferior product.