Temptation in Markets with no Commitment: Give-aways, Scare-aways and Reversals

I study a two period model where the buyer suffers from self-control problems and his level of temptation is private information. I derive the optimal behaviour of a seller that offers her product to a buyer. In period 1, the latter decides whether or not to “enter the store” based on the prices posted by the seller. In period 2 he decides how much of the product to buy, if any. Differently from the existing literature, I assume that the seller cannot commit to the prices posted in period 1. I show how, under this framework, the presence of tempted consumers and symmetric information can explain the existence of free vouchers offered by the seller to the consumer in exchange for entering the store. In contrast with classical contract theory, I show that the relatively untempted consumer (the “low type”) can be better off when information about his type is private than when the seller is fully informed. Moreover, the presence of self-control may induce the seller to exclude the relatively strongly tempted consumer (the “high type”) from the market.