Game-theoretic models for warranty and post-warranty maintenance with risk-averse service providers

Azmat Ullah, Muhammad Ayat, He Yi, Wenpo Huang, Jiang Wei

Research output: Contribution to journalArticlepeer-review


In this paper, a warranty-maintenance service contract is designed between a manufacturer and third-party agent who provide warranty and maintenance services respectively and may suffer from financial risks due to the demand uncertainty from consumers. We model the utility functions for the firms considering uncertain demand, risk attitude, and different options of warranty and maintenance service strategies. By using game theory, optimal sale price and warranty period for the manufacturer, whereas the optimal repair price or maintenance price for the third-party agent is explicitly derived by maximizing their expected utilities. Analytical results show that a more risk-averse manufacturer (or third-party agent) sets a lower price and gets lower utility as compared to a risk-neutral manufacturer (or third-party agent), which consequently leads to increases in product demand. The lower price decision of a more risk-averse player benefits a less risk-averse counterpart competitor in the market to set a higher price and get maximum utility. A numerical example is presented to illustrate the results.
Original languageEnglish
Pages (from-to)541-562
Number of pages22
JournalInternational Journal of Industrial Engineering : Theory Applications and Practice
Issue number5
Publication statusPublished - 4 Jan 2022
Externally publishedYes


  • warranty
  • maintenance
  • risk-averse players
  • non-cooperative game
  • demand uncertainty
  • utility theory


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