Optimal price and warranty decision for durable products in a competitive duopoly market


Manufacturers selling substitutive products often engage in stiff competitions. And the competition becomes more complicated in a duopoly market controlled by two large manufacturers. Surviving in such markets requires manufacturers to make advantaged marketing strategies to attract customers and expand their market shares. Numerous studies on strategic marketing competition concentrate on the issue of pricing. However, considering today’s marketing decisions, after-sales services like products warranty has emerged as an important promotional and competing instrument. For instance, in duopoly markets, which is common for durable products, the warranty has been used as a competition tool to increase sales. Notably, the interaction between prices and warranty is of great importance and should be an integral part of marketing strategies.

Even though providing warranties benefit both the transacting parties, it impossible to provide unlimited warranty due to trade-off effects between the operating costs and profits. Therefore, to provide better and competitive product warranties, organizations need to conduct market surveys to establish consumer behaviors and market patterns to obtain critical information use to determine the warranty conditions. Similarly, comprehensive knowledge of the interaction of different market members in a duopoly market and their impacts on the warranty decisions is still lacking.

Herein, Professor Chih-Chiang Fang from Zhaoqing University studied a competitive duopoly market to determine the warranty decisions and optimal durable products’ prices. The market study was carried out using a newly developed rational non-corporative game theory model to investigate the interactions amongst all the market members. Also, the marketing strategies regarding prices and warranty service decisions between the two manufactures were evaluated. The work is currently published in the journal, Reliability Engineering and System Safety.

In his approach, a duopoly market comprising of two key competing manufacturers was considered. The game theory model involved three key members: the competition firms, the local market and a technical supplier. The local market was characterized by high tariffs and stringent measures imposed by the government to protect local manufacturers from external competition. In this scenario, a technical supplier seeking to attain technical monopoly was tasked to supply both the firms with parts for manufacturing the substitutable products. Based on this information, the competitive equilibrium and coordination between the technical supplier and the firms and its impact on the pricing and post-sale services were analyzed and discussed.

The author found out that the two manufacturers’ decisions regarding prices and warranties reacted to each other. But upon attaining the duopoly market equilibrium, no firm could raise its prices or extend its warranty conditions to increase profits. Increased competition influenced a manufacturer’s warranty decisions if its warranty services were not better than its rival. Whereas the demand sensitivity exhibited a non-linear relationship with royalty with regard to the monopoly market of the supplier, the market share of a firm was linear to its equilibrium price. However, the equilibrium warranty was less sensitive to market share. Notably, the results emphasized the need to consider all possible maintenance and repair costs in making marketing decisions.

In summary, a game theory modelling of intensive competition between two manufacturers selling substitutable products and depending on the same technical supplier was reported. The symmetric and asymmetric scenarios enabled a comprehensive analysis of the interactions amongst the two duopoly firms and the technical supplier for a better understanding marketing strategy. Despite the stiff competition, the two firms could s provide different product prices and warranty services. In a statement to Advances in Engineering, the authors noted that the modelled scenario represented a real-life setting and provided insights that would benefit organizations and decision-makers in analyzing competitive equilibriums to make informed marketing decisions.

Optimal price and warranty decision for durable products in a competitive duopoly market - Advances in Engineering

About the author

CHIH-CHAING FANG is currently an associate professor in the School of Computer Science and Software at Zhaoqing University, Guangdong, China. He received his Ph.D. degree in the Department of Industrial and Information Management at National Cheng Kung University, Taiwan. His research interests include decision analysis, Bayesian statistical methods, software engineering and reliability engineering. Related papers have appeared in such professional journals as Naval Research Logistics, Decision Support Systems, Journal of Business Research, Reliability Engineering & Systems Safety, IEEE Transactions on Engineering Management, International Journal of Systems Science, Computers & Industrial Engineering, International Journal of Production Economics, International Journal of Production Research, Software Testing Verification & Reliability, and others.


Fang, C. (2020). Optimal price and warranty decision for durable products in a competitive duopoly marketReliability Engineering & System Safety, 203, 107068.

Go To Reliability Engineering & System Safety

Check Also

Moderation of thermoplastic composite crystallinity and mechanical properties through in situ manufacturing and post-manufacturing tempering: Part 1 – Mechanical characterisation - Advances in Engineering

Moderation of thermoplastic composite crystallinity and mechanical properties