Title: Extended Warranty Pricing in a Competitive Aftermarket Under Logit Demand

Authors:  Xiao-Lin Wang, Shizhe Peng, and Xiaoge Zhang

Abstract: It is common for multiple firms\textemdash such as manufacturers, retailers, and third-party insurers\textemdash to coexist and compete in the aftermarket for durable products. In this paper, we study price competition in a partially concentrated aftermarket where one firm offers multiple extended warranty (EW) contracts while the others offer a single one. The demand for EWs is described by the multinomial logit model. We show that, at equilibrium, such an aftermarket behaves like a combination of monopoly and oligopoly. Building upon this base model, we further investigate sequential pricing games for a durable product and its EWs to accommodate the ancillary nature of after-sales services. We consider two scenarios: one where the manufacturer (as the market leader) sets product and EW prices \emph{simultaneously}, and another where these decisions are made \emph{sequentially}. Our analysis demonstrates that offering EWs incentivizes the manufacturer to lower the product price, thereby expanding the market potential for EWs. Simultaneous product-EW pricing leads to a price concession on EWs compared to sequential pricing, effectively reducing the intensity of competition in the aftermarket. Overall, the competitiveness of an EW hinges on its ability to deliver high value to consumers at low marginal cost to its provider. While our focus is on EWs, the proposed game-theoretical pricing models apply broadly to other ancillary after-sales services.

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