Probabilistic price promotions without obligations

This paper studies the design of probabilistic price promotions where consumers through a lottery are either offered one of many promotional prices, including zero, or offered, but not obligated, to purchase products at the list price. Two behavioral biases are incorporated into the analysis: the cognitive bias zero-price effect, where consumers attach additional value to free products, and skepticism regarding the veracity of the lottery among a fraction of the consumers. The duopoly market consists of one firm operating the probabilistic price promotion and one firm operating a standard fixed price promotion. The equilibria regarding each firm’s optimal promotion parameters are derived. It is shown that a simple lottery, wherein consumers either receive the product for free or are offered to pay the fixed list price, is more profitable than a complex lottery with many promotional prices. Moreover, firms should only offer probabilistic price promotions when the zero-price effect is larger than a threshold, which decreases in the fraction of consumers who trust the promotions. This offers key managerial implications: firms with excellent reputations should offer the simple lottery to capitalize on the zero-price effect, while firms with mediocre reputations should prioritize fixed price promotions. Several robustness analyses and extensions to the base model are considered, including government lottery certification, symmetric promotion strategies, and partial market coverage.