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Yang Zhou, Jianwen Chen, Ruipeng Wei · 2026-07-06
Using a simulated market where one profit-maximizing institutional agent trades against 20,000 herding retail traders, the authors find the agent spontaneously learns a repeating 'predatory' strategy that cycles through the market roughly 8-11 times over 2000 days, earning around +38% on average (best +51%). They show mathematically that these manipulation cycles only appear when price impact follows a square-root law; with linear price impact the cycles vanish and the market stays stable.
Why it matters: The study illustrates how a large, adaptive player can extract returns by exploiting predictable herding and the square-root relationship between trade size and price movement — a dynamic worth being aware of when trading crowded or momentum-driven markets. It suggests that market instability and manipulation cycles may be an emergent structural feature tied to how impact scales, not just bad actors.
⚠ This is a stylized agent-based simulation and mathematical theory, not evidence from real market data, so its dynamics may not transfer to live trading.
We study a minimal agent-based market in which a single evolutionary-optimized institutional agent interacts with 20{,}000 herding retail traders. The agent spontaneously discovers a multi-cycle predatory strategy, producing 8--11 complete cycles over 2000 trading days with total portfolio return of $+51\%$ (best of 20 seeds; mean $+37.7\%$). Mean-field reduction maps the system onto a nonlinear oscillator that undergoes two distinct bifurcations: a continuous Hopf transition as institutional capital exceeds a critical threshold $C_c$, with oscillation amplitude $A \propto (C-C_c)^α$ where $α$ is consistent with the standard prediction of $1/2$; and a discontinuous fold transition in the herding-scale parameter space. The limit cycle persists even at $β= 0$: position-tracking feedback coupled with square-root price impact creates a self-sustained nonlinear oscillator requiring no retail herding. Square-root impact is shown to be necessary: linear impact eliminates the Hopf bifurcation entirely and renders the retail market unconditionally stable. Manipulation cycles thus emerge as the optimal-control solution of a nonlinear dynamical system, and a structural analogy to Maxwell's demon frames the agent as an information-processing controller that reduces the entropy rate of the price process.
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