Mathematical models of warranty policies: a game theory perspective

Abstract

This thesis presents two mathematical models of pricing for warranty policies considering a game theory approach. The first model is a two-person game. The consumer outsources maintenance actions to the agent (maintenance agent), who shows four warranty options with different coverage characteristics. Equilibrium strategies for each decision-maker are obtained via the subgame-perfect Nash equilibrium. In the second model, we add the manufacturer in the modeling. Thus, a three-person game is formulated. The manufacturer defines the sale price of the product (including the base warranty costs), whereas the agent prices maintenance services. Equilibrium strategies are given through a combination of cooperative and non-cooperative solutions. The model brings a coalition between the manufacturer and the agent, and the Shapley value redistributes the payoffs and sets up the equilibrium prices. In both models, we perform a sensitivity analysis with the model parameters and apply computer simulation to estimate the expected value of warranty costs for some warranty policies.