Competitive Dealing Strategy and Deal Value Escalation

This note is an extension of "A Mathematical Model for Price Promotions" (Kinberg, Rao and Shakun [Kinberg, Yoram, Ambar G. Rao, Melvin F. Shakun. 1974. A mathematical model for price promotions. Management Sci. 20 948--959.]). That paper derived the revenue maximizing deal value for a firm in a monopolistically competitive, price (quality) partitioned market having two premium brands and consumers whose responses to deals are heterogeneous. This "optimal" deal value was derived under the assumed condition of no competitive dealing. When competitive dealing was considered, both dealing brands were assumed to offer the same "optimal" deal value. By extending the work of KRS to include a number of competitors sufficiently large that at least one is dealing in each period, this paper shows that a reactive dealing strategy based on a single "optimal" deal value produces negative profits and will not produce a stable equilibrium.