A game theoretic approach with pricing and cooperative advertisement and warranty period in a two-level supply chain

¹ School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
² Department of Industrial Engineering, Istinye University, Istanbul, Turkey
³ Tecnológico de Monterrey, School of Engineering and Sciences, E. Garza Sada 2501 Sur, Monterrey, C.P. 64849, Nuevo León, México
⁴ Regent Education and Research Foundation, Barrackpore, 700121 Kolkata, India

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 4 December 2024
Accepted: 24 November 2025

Abstract

Cooperative advertisement is one of the market strategies in which the manufacturer pays for a part of the retailer’s local advertisements. Offering warranty period to customers is another market strategy for improving company market share. This paper develops a two level supply chain with one manufacturer and one retailer in which warranty period costs such as local advertisements costs are shared among supply chain members. It means that, both a cooperative advertisement and a cooperative warranty period are considered at the same time. So, there are two participation rates in the two-level supply chain model. But unlike the previous research works, this paper investigates the effect of these two participation rates on other important variables and display the relationship among these rates and the variables trend. This is important for decision makers, because investigating about these trends improve their insights about cooperative relation in supply chain. The cooperative two-level supply chain model considers a linear demand function and a nonlinear products return rate. A game theoretic approach is used to study the cooperative two-level supply chain model. Basically, three games including Nash, manufacturer Stackelberg and retailer Stackelberg are applied. The main purpose of this paper is to improve the insights of decision makers and help them to make appropriate decisions when they incorporate cooperative advertisement and a cooperative warranty period.