The Invisible Handshake: Persistent Overpricing by Adaptive Market Agents

Battle Count: 62

Highly relevant to quantitative trading. The paper directly addresses how adaptive algorithmic trading agents (market makers and takers) can endogenously generate persistent price distortions through decentralized learning without explicit coordination. The square-root price impact model is standard in market microstructure. The game-theoretic decomposition into competitive and collaborative components provides deep insight into why algorithmic trading systems may sustain overpricing. The finite-time convergence results for PSGA are directly applicable to understanding the dynamics of learning-based trading algorithms. The distinction between positive-net-supply and zero-net-supply markets has practical implications for different asset classes. The paper connects to the growing literature on algorithmic collusion and AI-driven trading risks highlighted by BIS and IMF reports.

High complexity. The theoretical framework involves constrained stochastic games, Markov game analysis, strategy parameterization with feasibility constraints, game decomposition (competitive/collaborative), stochastic convergence proofs with sub-Gaussian martingale concentration, and infinite-horizon optimization. Implementing the trading protocol and PSGA updates is moderate, but understanding and extending the theoretical results requires deep expertise in game theory, stochastic analysis, and market microstructure. The feasibility boundary functions f_alpha and f_beta involve solving cubic equations. The proof techniques (optional stopping, dominated convergence, martingale concentration) are advanced.

The paper is primarily theoretical with complete mathematical proofs provided in the appendix. Simulations (Figures 1 and 2) are described with specific parameter choices (k_alpha=k_beta=v_alpha=v_beta=1/2, phi=0.7 for overpricing, phi=0.3 for underpricing, sigma=0.3 for shocks, c=i=0, C=I=1). However, no code repository is provided. The theoretical framework is fully self-contained with all definitions, lemmas, and theorems stated and proved. Reproducing the simulations would require implementing the trading protocol and PSGA updates from the pseudocode, which is feasible but non-trivial.