We address infinite-horizon models for oligopolies with competing retailers under demand uncertainty. We characterize the equilibrium behavior which arises under simple wholesale pricing schemes. More specifically, we consider a periodic review, infinite-horizon model for a two-echelon system with a single supplier servicing a network of competing retailers. In every period, each retailer faces a random demand volume, the distribution of which depends on his own retail price as well as those charged by possibly all competing retailers. We also derive various comparative statics results regarding the impact several exogenous system parameters (e.g., cost or distributional parameters) have on the equilibrium decisions of the retailers as well as their expected profits. We show that certain monotonicity properties, engrained in folklore as well as in known inventory models for centralized systems, may break down in decentralized chains under retailer competition. Our results can be used to optimize the aggregate profits in the supply chain (i.e., those of the supplier and all retailers) by implementing a specific wholesale pricing scheme.
Bernstein, Fernando, and Awi Federgruen. "Dynamic inventory and pricing models for competing retailers." Naval Research Logistics 51, no. 2 (March 2004): 258-274.
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