Cooperative and Non-Cooperative Strategies in Product Warranty Pricing: A Hierarchical Game Approach

Henrique Santos and Thyago Nepomuceno ()
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Henrique Santos: Programa de Pós-Graduação em Biometria e Estatística Aplicada, Federal Rural University of Pernambuco, Recife 52171-900, Brazil
Thyago Nepomuceno: Department of Statistics, Federal University of Pernambuco, Recife 50740-560, Brazil

Games, 2025, vol. 16, issue 4, 1-10

Abstract: This paper analyzes the pricing dynamics of product warranties by developing a three-player hierarchical game model involving a manufacturer, an independent service agent, and a consumer. The model provides a scenario where the manufacturer and the agent form a coalition to coordinate pricing strategies, while interacting non-cooperatively with the consumer. In this framework, the manufacturer sets the product’s sale price, including the base warranty, while the agent determines the price of extended maintenance services. The key contribution is the application of the Shapley value to equitably distribute the coalition’s profits based on each member’s contribution—a novel approach in the warranty pricing literature. We detail the characteristic functions that define the coalition’s structure and present computer simulations to estimate the expected costs associated with maintenance services. A comprehensive sensitivity analysis is applied to report how changes in parameters influence equilibrium strategies and players’ payoffs. The results provide strategic insights into how manufacturers and agents can coordinate to optimize pricing, capture consumer surplus, and improve decision-making in warranty service markets.

Keywords: hierarchical game theory; product warranty; pricing strategy; cooperative game; non-cooperative game; Shapley value; manufacturer–agent coalition; service contracts; game-theoretic modeling; consumer surplus (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2025
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