A Subgame Perfect Approach to a Multi-Period Stackelberg Game with Dynamic, Price-Dependent, Distributional-Robust Demand

Abstract

This paper investigates a multi-periodic channel optimization facing uncertain, price dependent, and dynamic demand. The picture of the market uncertainty is incomplete, and only the price and time-dependent mean and standard deviation are known and may depend on the price history. The actual demand distribution itself is unknown as is typically the case in real world problems. An algorithm finding the optimized decentralized channel equilibrium is developed when the downstream member optimizes her expected profit stream by a distributional-robust approach, and the upstream member (leader) considers it as the follower’s reaction function. The algorithm allows for strategic decisions whereby the current demand is scaled by the previous price setting.