Competition in posted prices with stochastic discounts

We study price competition between firms over public list or posted prices when a fraction of consumers (termed 'bargainers') can subsequently receive discounts with some probability. Such stochastic discounts are a feature of markets in which some consumers bargain explicitly; of markets in which sellers use the marketing practice of couponing; and of markets in which sellers offer both simple-to-understand tariffs (the posted prices) alongside complex or opaque tariffs that might offer a discount. Even though bargainers receive reductions off the posted prices, the potential to discount dampens competitive pressure in the market by reducing the incentive to undercut a rival's posted price, thus raising all prices and increasing profits. Welfare falls because of the stochastic nature of the discounts, which generates some misallocation of products to consumers. We also find that stochastic discounts facilitate collusion by reducing the market share that can be gained from a deviation