Omar Besbes

Product assortment and price competition with informed consumers

Coauthor(s): Denis Saure.

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Abstract:
We study equilibrium behavior for product assortment and price competition in a duopoly of retailers in the presence of informed consumers, i.e., when consumers have full knowledge of the retailers' offerings when making purchase decisions. We study two settings: i.) assortment-only competition where prices are exogenously fixed, and ii.) joint assortment and price competition. In both settings, retailers have a set of products from which to select an assortment and face a display constraint, and the resulting demand is assumed to follow a multinomial Logit model. We separate the case where retailers have only exclusive products, i.e., the sets of available products do not overlap, and the case where there might be common products, highlighting the implications of the latter. For the case of assortment competition with exclusive products, we prove existence of an equilibrium and provide a bound on the number of equilibria. In addition, we show that when multiple equilibria exist, retailers always prefer the same equilibrium. When some common products are available, we provide sufficient conditions for existence of an equilibrium and we show that in general an equilibrium may fail to exist, or the number of equilibria may increase exponentially with the display capacity of the retailers. For the case of joint assortment and price competition, we show that at most one equilibrium exists. It is guaranteed to exist in the case of exclusive products; in general, we provide a simple procedure to either prove no equilibrium exists or find the unique equilibrium. Moreover, our analysis indicates that assortment competition broadens each retailer's assortment selection and decreases prices, relative to the monopolistic setting.

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