bThis paper aims at showing how the game theory can be applied to the quantitative study of extended warranty (EW). This kind of after-sales service represents an additional noncompulsory coverage, which the consumer can or not buy after the acquisition of some device, starting subsequently to the end of the base warranty (BW) period. Thus, a model, in which two players interact, is shown, i. e. the original equipment manufacturer (OEM), in charge of assigning prices to the equipment and to the extended warranty service; and the customer (owner of the device). The way, in which the parts interact, is modeled through the Stackelberg leadership game, which was originally applied in the analysis of the oligopolies competition market. In this particular model, the leader represents the OEM and the follower is the customer, where the OEM's goal is to find a certain price structure to maximize his profit and consequently influence the buyer's decision. Through this adaptation, the strategies and payoffs of players are defined. The robustness of the model is due to incorporating elements of the economic theory (consumer's surplus, producer's surplus, consumer's reservation price, choice under uncertainty, maximum profit and contingent consumption plan) and elements of the reliability theory (probability of failure and non-repairable systems). Additionally, a numerical example and a sensitivity analysis of parameters are presented to highlight the model. Finally, this research systematizes the steps of Stackelberg game under the modeling of extended warranty (EW) as well.

This essay presents a novel look at Murthy and Asgharizadeh's study (Murthy & Asgharizadeh, 1998). The authors developed a decision problem applied to maintenance outsourcing involving two decision-makers (players). If a consumer buys a product, then outsources the maintenance actions to a maintenance agent (agent) who offers two maintenance options; a maintenance contract that holds a penalty clause which is activated if the agent's time to repair is higher than a specified time, and services on-demand. The model yields equilibrium strategies based on the subgame-perfect Nash equilibrium. The agent defines the optimal pricing structure for the maintenance options considering the equipment's useful life while the consumer maximizes their expected payoff by choosing one maintenance option. Our contribution to this research branches in three ways. First, once the model deals with random variables, it represents a stochastic optimization problem. We propose a different approach to estimate this penalty time by using the Monte Carlo method. The second contribution is to present a formal definition of this decision problem as a game, emphasizing the game theory's components. Finally, we reinterpret the players' equilibrium strategies.