Since traffic jams are ubiquitous in the modern world, optimizing the behavior of traffic lights for efficient traffic flow is a critically important goal. Though most current traffic lights use simple heuristic protocols, more efficient controllers can be discovered automatically via multiagent reinforcement learning, where each agent controls a single traffic light. However, in previous work on this approach, agents select only locally optimal actions without coordinating their behavior. This paper extends this approach to include explicit coordination between neighboring traffic lights. Coordination is achieved using the max-plus algorithm, which estimates the optimal joint action by sending locally optimized messages among connected agents. This paper presents the first application of max-plus to a large-scale problem and thus verifies its efficacy in realistic settings. It also provides empirical evidence that max-plus performs well on cyclic graphs, though it has been proven to converge only for tree-structured graphs. Furthermore, it provides a new understanding of the properties a traffic network must have for such coordination to be beneficial and shows that max-plus outperforms previous methods on networks that possess those properties.