The possibility of `tacit collusion', in which interactions across market making algorithms lead to an outcome similar to collusion among market makers, has increasingly received regulatory scrutiny. We model the interaction of market makers in a dealer market as a stochastic differential game of intensity control with partial information and study the resulting dynamics of bid-ask spreads. Competition among dealers is modeled as a Nash equilibrium, which we characterise in terms of a system of coupled Hamilton-Jacobi-Bellman (HJB) equations, while Pareto optima correspond to collusion. Using a decentralized multi-agent deep reinforcement learning algorithm to model how competing market makers learn to adjust their quotes, we show how the interaction of market making algorithms may lead to tacit collusion with spread levels strictly above the competitive equilibrium level, without any explicit sharing of information. Joint work with Wei Xiong (Oxford)