A Stackelberg-Nash model for new product design

Abstract

Existing conjoint approaches to optimal new product design have focused on the Nash equilibrium concept to model competitive reactions. Whereas these approaches have treated all competing firms equally as Nash players, one firm may have an advantage over its rivals, e.g., more pre-experience on competitors’ behavior and/or a first-mover advantage. This paper proposes a Stackelberg-Nash (leader-followers) model which can accomodate such information for decision making. The optimal product design problem is formulated from the perspective of a profit-maximizing new entrant (the leader) who wants to launch a brand onto an existing product market and acts with foresight by anticipating price-design reactions of the incumbent firms (the Nash followers). In the absence of closed-form solutions, we use a sequential iterative procedure to compute a Stackelberg-Nash equilibrium and to establish its uniqueness. The new conjoint model is illustrated under several competitive scenarios and price, design and profit implications are compared to a simple Nash equilibrium model. We find that a Stackelberg leader strategy may not only yield a much higher profit for the new entrant than a Nash strategy, but may also lead to strong profit asymmetries between competitors with still higher profits for the incumbent firms. In other words, the incumbent firms may also benefit strongly from a new entrant choosing a Stackelberg leader strategy.