Game-Theoretic Market Making with Multi-Agent Reinforcement Learning Validation

Abstract

Electronic market makers provide liquidity by submitting bid and ask quotes. When posting quotes, market makers must simultaneously manage trade-offs between spread capture and adverse selection. These trade-offs become significantly more complex when multiple dealers compete for shared order flow while also receiving different private signals. This thesis considers a dynamic game of two-dealer market-making with heterogeneous private signals. One dealer receives private information about the asset’s latent fundamental value while the other receives private information about a latent toxicity state which determines the probability of informed order flow. Both dealers observe a noisy public mid-price, carry inventory over time, and compete via best-quote execution. This work contributes to the theoretical understanding of this game through a combination of game-theoretic analysis and theory-aligned multi-agent reinforcement learning. We find that dealers’ distinct informational advantages impact quoting behavior through different channels: toxicity information primarily affects spreads, value information primarily affects quote placement, and inventory risk primarily affects skew. Against a benchmark with zero inventories and symmetric information, learned policies qualitatively move toward satisfying the zero-profit condition, though equilibrium spreads are learned to be wider than in theory. Under the full environment, learned posting policies are monotone in effective ask costs and bid values, and closely mirror several of the theory’s comparative static predictions.