Product Line Design with Quantal Consumer Preferences

This paper studies how a firm designs a product line that motivates consumers to deliberate to infer their preferences and buy the product that matches the perceived preferences by deliberation. Some consumers cannot determine their true preferences after deliberation and instead perceive a wrong preference as their own. The statistics describing the distribution of preference perception after deliberation are defined as quantal preferences. By considering the quantal preferences, the firm is only able to design a product line that makes sure the population of consumers with same true preference willingly and truthfully participate the purchasing activity. Our research shows that the equilibrium properties of a screening contract (product line in our context) have been essentially altered by the quantal preferences compared with corresponding properties in a standard screening contract. With quantal preferences, at equilibrium, firm sacrifices part of their profit to reimburse each group of consumers to participate the purchase. Quantal preferences introduce two new incentives into the product line: limiting surplus losses and driving consumer to deliberate the true preference as much as possible. Different incentives can interrelate, e.g. the incentive motivating consumers to truthfully determine their perceived preferences and hence sorting different populations of consumers by the perceived preferences interacting the incentive limiting surplus losses, where deliberation cost adjusts which incentive is stronger. With quantal preferences, high type product can attract low preference consumers. The quality of high type product can be negative. The profit of high type or low type product can be negative, and the surplus of high type or low product can be negative as well. If only one type of product can be produced, it can be the low type product.