Competitive Assortment and Price Optimization

In the models that we studied thus far, we considered the decisions made by a single firm. The implicit assumption in our development was that the other firms do not react to the decisions of each other. Naturally, this is almost never the case. When a firm decreases its prices, fearing loss of customers, its competitors may also decrease its prices. Both online and brick-and-mortar retail stores consider the assortments offered by the other stores when making planning their assortments. There is vast literature on modeling competition. Nevertheless, despite the fact that competition is the rule rather than an exception and there is vast literature on modeling competition, the development of operational models that can drive real-time decision making under competition is in its infancy. In most operational models, it is often the case that the competition is ignored or modeled rather simplistically. Perhaps, the most important reason for this is that explicitly modeling competition often times results in intractable models. Thus, for the sake of computational tractability, the reactions of the other firms are ignored. Furthermore, the data that drive the operational models are often collected in a competitive environment, and one usually naively hopes that building a noncompetitive model driven by data collected in a competitive environment will take care of the competition itself, but of course, this hope is not based on any scientific evidence.