Probabilistic price promotions without obligations

Highlights • We analyze duopoly randomized pricing/lottery game with a potentially free product • Firm offering promotion with free products given behavioral bias zero price effect • We derive the equilibrium prices and optimal lottery parameters • Extensions: government certificate; symmetric game; binomial customer valuation; • Extensions: positive production cost; sequential market dynamics; partial market coverage 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 a 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: symmetric promotion strategies; government lottery certification; sequential market dynamics; positive production cost; and heterogeneous consumer valuations.