Scandinavian Working Papers in Business Administration

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2023/4: A Subgame Perfect Approach to a Multi-Period Stackelberg Game with Dynamic, Price-Dependent, Distributional-Robust Demand

Mahnaz Fakhrabadi () and Leif K. Sandal ()
Additional contact information
Mahnaz Fakhrabadi: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Leif K. Sandal: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway

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.

Keywords: Multi-Periodic problem; Stochasticity; Stackelberg Game; Subgame Perfect Distributional-Robust Approach; Supply Chain Management; Price-History Dependent Dynamic Demand

JEL-codes: C61; C62; C63; C72; C73; D81

Language: English

17 pages, March 22, 2023

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