Reputation Building under Observational Learning

A patient seller interacts with a sequence of myopic consumers. Each period, the seller chooses the quality of his product, and a consumer decides whether to trust the seller after she observes the seller’s actions in the last $K$ periods (limited memory) and at least one previous consumer’s action (observational learning). However, the consumer cannot observe the seller’s action in the current period. With positive probability, the seller is a commitment type who plays his Stackelberg action in every period. I show that under limited memory and observational learning, consumers are concerned that the seller will not play his Stackelberg action when he has a positive reputation and will play his Stackelberg action after he has lost his reputation. Such a concern leads to equilibria where the seller receives a low payoff from building a reputation. I also show that my reputation failure result hinges on consumers’ observational learning.