  We study auction-theoretic scheduling in cellular networks using the idea of
mean field equilibrium (MFE). Here, agents model their opponents through a
distribution over their action spaces and play the best response. The system is
at an MFE if this action is itself a sample drawn from the assumed
distribution. In our setting, the agents are smart phone apps that generate
service requests, experience waiting costs, and bid for service from base
stations. We show that if we conduct a second-price auction at each base
station, there exists an MFE that would schedule the app with the longest queue
at each time. The result suggests that auctions can attain the same desirable
results as queue-length-based scheduling. We present results on the asymptotic
convergence of a system with a finite number of agents to the mean field case,
and conclude with simulation results illustrating the simplicity of computation
of the MFE.
