# A Mean Field Games Approach to Scheduling in Cellular Networks

We study auction-theoretic scheduling in cellular networks using the idea of a mean field equilibrium (MFE). Here, agents model their opponents through an assumed distribution over their action spaces, and play the best response action against this distribution. We say that the system is at MFE if this best response action turns out to be a sample drawn from the assumed distribution. In our setting, the agents are smartphone apps that generate service requests, have costs associated with waiting, and bid against each other for service from base stations. The users of the apps spend a geometrically distributed amount of time on each app, and then move on to another. We show that in a system in which we conduct a second-price auction at each base station and schedule the winner at each time, there exists an MFE that will schedule the user with highest value at each time. We further show that the scheme can be interpreted as a weighted longest queue first type policy. The result suggests that auctions can implicitly attain the same stabilizing effects as queue-length based scheduling. We will also present some results on the convergence between a system with a finite number of agents to a mean field case as the number of agents become large. Finally, we will spend some time discussing our other recent work in the space of game theory and content distribution networks.