“Tacit bundling” among rivals: Limited-availability bargains for loss-averse consumers

This paper derives a stochastic discount strategy that encourages the joint consumption of two partial-substitute goods. The seller of the less valuable product offers a limited-availability discount to consumers with reference-dependent preferences à la Kőszegi and Rabin (2006). The stochastic discount introduces uncertainty in the consumers’ outcomes and increases their willingness to pay. Due to market competition, such stochastic pricing is effective only when it induces consumers to purchase both products. The other seller, who can only use deterministic pricing, tacitly consents as he has no benefit from engaging in a price war. Thus, a collusive outcome – which harms consumer welfare – is achieved without any explicit coordination between the two sellers.