The weight of the crowd, social information credibility, and firm strategy

When considering a purchase, consumers often augment their private information about a product with anonymous online social information (reviews, etc.). We examine the impact on firm strategy of how consumers weight these two information sources—private and social—in their purchase decisions. An increase in weight on private information always results in higher prices at the interior equilibrium. However, the effects on profits, consumer, and total surplus are nonmonotonic: all increasing with the weight on private information when weight is high but decreasing when weight is low. Profit and surplus decrease with weight when weight is low because a marginal increase in a low weighting leads to a contraction of demand. The dynamic reverses when weight is high. Besides weighting of information sources, our model incorporates the questionable credibility of social information. A firm's optimal investment to improve social information credibility depends on whether consumers process information in a Bayesian or non‐Bayesian manner. We show that, compared to Bayesian consumers, non‐Bayesian consumers endogenously trust (distrust) social information from firms with high(low)‐positivity ratings. This distinction in information processing results in a stark contrast in how firms manage social information credibility: when facing Bayesian consumers, with an increase in the positivity of its social information, a firm with high(low) positivity spends less (more) to improve credibility. On the contrary, when facing non‐Bayesian consumers, a firm with high(low) positivity spends more (less) to improve credibility. Product quality also affects optimal credibility investment, following an inverted U‐shape.