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Coopetition between LTE unlicensed and Wi-Fi: A reverse auction with allocative externalities

Motivated by the recent efforts in extending LTE to the unlicensed spectrum, we propose a novel spectrum sharing framework for the coopetition (i.e., cooperation and competition) between LTE and Wi-Fi in the unlicensed band. Basically, the LTE network chooses to work in one of the two modes: in the competition mode, it randomly accesses an unlicensed channel, and interferes with a Wi-Fi access point; in the cooperation mode, it onloads a Wi-Fi access point's traffic in exchange for the full access of the corresponding channel. Because the LTE network works in an interference-free manner in the cooperation mode, it can achieve a much larger total data rate (comparing to the competition mode) to serve both its own users and the Wi-Fi users under proper channel conditions. To achieve the maximum potential of this novel coopetition framework, we design a reverse auction mechanism, where the LTE provider is the auctioneer (buyer), and the Wi-Fi access point owners (APOs) are the bidders who compete to sell their channels to the LTE provider. An APO's bid indicates the data rate that it would like the LTE provider to offer in the cooperation mode. We show that the auction involves the allocative externalities, i.e., the cooperation between the LTE provider and an APO benefits other APOs who are not directly involved in this cooperation. As a result, a particular APO's bidding strategy is affected by its belief about other APOs' bidding strategies. This makes our analysis much more challenging than that of the standard second-price auction, where bidding truthfully is a weakly dominant strategy. We characterize the APOs' unique equilibrium bidding strategies, and analyze the LTE provider's optimal reserve rate that maximizes its payoff for a general APO type distribution. Our analysis shows that only when the LTE throughput exceeds a threshold, the LTE provider will choose a reasonably large reserve rate to cooperate with the APOs; otherwise, it will restrict the reserve rate to a small value and work in the competition mode.