We study auction-theoretic scheduling in cellular systems using the idea of a mean field equilibrium, in which agents model their opponents through a distribution over their action spaces, and optimize against this distribution. Here, the agents are apps that generate service requests, have costs associated with waiting, and bid against each other for service. Users spend an geometrically distributed amount of time on each app, and then move on to another. We show that conducting a second-price auction and scheduling the winner at each time results in an MFE that will provide the correct amount of service for each application, hence showing that the system is self-stabilizing. The result suggests that auctions can attain the same stabilizing effects as queue-length based scheduling.