Construction of Equilibria in Strategic Stackelberg Games in Multi-Period Supply Chain Contracts

Reza Azad Gholami (), Leif Sandal () and Jan Ubøe
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Reza Azad Gholami: Department of Business and Management Science, Norwegian School of Economics, Helleveien 30, 5045 Bergen, Norway

Games, 2022, vol. 13, issue 6, 1-26

Abstract: Almost every supplier faces uncertain and time-varying demand. E-commerce and online shopping have given suppliers unprecedented access to data on customers’ behavior, which sheds light on demand uncertainty. The main purpose of this research project is to provide an analytic tool for decentralized supply channel members to devise optimal long-term (multi-period) supply, pricing, and timing strategies while catering to stochastic demand in a diverse set of market scenarios. Despite its ubiquity in potential applications, the time-dependent channel optimization problem in its general form has received limited attention in the literature due to its complexity and the highly nested structure of its ensuing equilibrium problems. However, there are many scenarios where a single-period channel optimization solution may turn out to be myopic as it does not consider the after-effects of current pricing on future demand. To remedy this typical shortcoming, using general memory functions , we include the strategic customers’ cognitive bias toward pricing history in the supply channel equilibrium problem. In the form of two constructive theorems, we provide explicit solution algorithms for the ensuing Nash–Stackelberg equilibrium problems. In particular, we prove that our recursive solution algorithm can find equilibria in the multi-periodic variation of many standard supply channel contracts such as wholesale, buyback, and revenue-sharing contracts.

Keywords: game theory; Stackelberg games; supply chain management; stochastic demand; behavioral newsvendor; price-setting newsvendor (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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