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We study the ability of autonomous vehicles to improve the throughput of a bottleneck using a fully decentralized control scheme in a mixed autonomy setting. We consider the problem of improving the throughput of a scaled model of the San Francisco-Oakland Bay Bridge: a two-stage bottleneck where four lanes reduce to two and then reduce to one. Although there is extensive work examining variants of bottleneck control in a centralized setting, there is less study of the challenging multi-agent setting where the large number of interacting AVs leads to significant optimization difficulties for reinforcement learning methods. We apply multi-agent reinforcement algorithms to this problem and demonstrate that significant improvements in bottleneck throughput, from 20\% at a 5\% penetration rate to 33\% at a 40\% penetration rate, can be achieved. We compare our results to a hand-designed feedback controller and demonstrate that our results sharply outperform the feedback controller despite extensive tuning. Additionally, we demonstrate that the RL-based controllers adopt a robust strategy that works across penetration rates whereas the feedback controllers degrade immediately upon penetration rate variation. We investigate the feasibility of both action and observation decentralization and demonstrate that effective strategies are possible using purely local sensing. Finally, we open-source our code at https://github.com/eugenevinitsky/decentralized_bottlenecks.