A Stackelberg Game Theory Approach to Optimize Warranty Length, Upgrade Level and Sale Price for Risk-Averse Buyers of Second-Hand Products

Customers are often uncertain about the quality and durability of used or second-hand products. In order to reduce the customers’ uncertainly, the dealers are currently carrying out some upgrade actions as well as offering reasonable warranties for second-hand products before releasing them to the market. Applying excessive upgrades and/or offering long warranty periods may cause the prices to be uncompetitive within the second-hand product markets. Therefore, it is crucial for the dealers to optimize the upgrade strategy, warranty policy and selling price of second-hand products. This paper presents a Stackelberg game theory model to determine the optimal upgrade level, warranty length and sale price for second-hand products in the case when the customers are risk-averse. The conflict between the customers’ expected costs and the dealer’s expected profit associated with a second-hand product sold with one-dimensional warranty and post-warranty contact will be modeled. The Karush–Kuhn–Tucker (KKT)’s optimality condition of the lower level problem is used to solve the model. Finally, a numerical example is provided to illustrate the proposed model and a sensitivity analysis is conducted to assess the effects of model parameters on the optimal problem solution.