At present, the crowdsourcing-based indoor navigation system (CINS) has attracted extensive attention from both industry and academia owing to its low-cost and high-accuracy performance. Unfortunately, the system that relies on crowdsourced data is vulnerable to the collusion attack, which leads to severe security issues. To address the security issues in the CINS, we propose to utilize a fully trusted fog server platform to advocate secure transactions between service requesters and responders. First, we propose a novel reputation incentive mechanism based on the behaviors of responders. Then, we employ the offensive and defensive game to model the interactions between the fog server platform and the responders, whereby a social welfare optimization problem is formulated to maximize the social welfare of the system. Next, the game equilibriums are found by using the replicator dynamic equation while the game stability is discussed. Finally, the simulation results show that the proposed mechanism can effectively encourage responders to provide positive navigation services and obtain more social welfare of the system compared with the conventional mechanisms.