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Dynamic Pricing and Inventory Control: Uncertainty and Competition

Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, Illinois 60607
Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts
elodie{at}uic.edu
georgiap{at}mit.edu

In this paper, we study a make-to-stock manufacturing system where two firms compete through dynamic pricing and inventory control. Our goal is to address competition (in particular a duopoly setting) together with the presence of demand uncertainty. We consider a dynamic setting where multiple products share production capacity. We introduce a demand-based fluid model where the demand is a linear function of the price of the supplier and of her competitor, the inventory and production costs are quadratic, and all coefficients are time dependent. A key part of the model is that no backorders are allowed and the strategy of a supplier depends on her competitor's strategy. First, we reformulate the robust problem as a fluid model of similar form to the deterministic one and show existence of a Nash equilibrium in continuous time. We then discuss issues of uniqueness and address how to compute a particular Nash equilibrium, i.e., the normalized Nash equilibrium.

Subject classifications: game theory; optimization under uncertainty; robust optimizations; normalized Nash equilibrium; dynamic pricing.
History: Received January 2007; revision received January 2009; accepted January 2009.