Autonomous vehicle (AV) technology is maturing, and AVs are being test-driven on public roads. A promising intersection control policy, tilebased reservation (TBR), proposed by Dresner and Stone in 2004, could improve intersection capacity beyond the capabilities of optimized traffic signals. Although TBR has been studied in several microsimulation models, it has yet to be analyzed under user equilibrium behavior. In this study, TBR was modeled in the dynamic traffic assignment to draw on the extensive literature on vehicle routing behaviors. With the proposed model, TBR can be computationally simulated on large city networks, with the goal of solving the traffic assignment problem. TBR also arbitrarily prioritizes vehicle movement, and high-value-of-time travelers may be able to gain priority through intersection auctions, as suggested by the literature. An in-depth study of simple intersection auctions found that much of the benefit (over first-come, first-served prioritization) resulted from the randomizing effect of auctions giving larger queues of vehicles greater shares of the intersection capacity.