A Distributional Robust Analysis of Buyback and Cap-and-Trade Policies

Abstract

This study delves into a dynamic Stackelberg game comprised of a manufacturer and a retailer, operating in an environment with fluctuating demand and price-dependent consumer behavior. The multi-period optimization challenges the manufacturer to strategically set wholesale and buyback prices, while the retailer determines the retail price and order quantities within a single contract. In this dynamic framework, the players operate under the constraints of a cap-and-trade policy, with limited knowledge of demand distributions, characterized only by mean and standard deviation parameters. To address this inherent uncertainty, we employ a distributionally robust approach. Additionally, we explore the enduring effects of historical decisions on present-day demand, reflecting a memory-like market behavior. Through numerical examples, we illuminate the influence of buyback contracts and cap-and-trade policies on decision-making processes within this setting.