Tremendous efforts have been made to protect the location privacy of mobile users. Some of them, e.g., k-anonymity, require the participation of multiple mobile users to impede the adversary from tracing. These participating mobile users constitute an anonymity set. However, not all mobile users are seriously concerned about their location privacy. Therefore, to achieve k-anonymity, we need to provide incentives for mobile users to participate in the anonymity set. In this paper, we study the problem of incentive mechanism design for k-anonymity location privacy. We first consider the case where all mobile users have the same privacy degree requirement. We then study the case where the requirements are different. Finally, we consider a more challenging case where mobile users can cheat about not only their valuations but also their requirements. We design an auction-based incentive mechanism for each of these cases and prove that all the auctions are computational efficient, individually rational, budget-balanced, and truthful. We evaluate the performance of different auctions through extensive simulations.