🤖 AI Summary
This study investigates the emergence of endogenous manipulation cycles in a learning-based trading agent market and their impact on price dynamics. By constructing a minimal agent-based model comprising one institutionally optimized evolutionary agent and twenty thousand retail traders, and leveraging mean-field theory to reduce it to a nonlinear oscillator system, the work reveals—for the first time—that a square-root price impact is a necessary condition for such endogenous cycles. Remarkably, self-sustained limit cycles arise solely from position feedback and square-root impact, even without herding by retail traders, functioning analogously to a Maxwell’s demon–like information controller. Over 2,000 trading days, experiments consistently reproduce 8–11 cycles, yielding an average cumulative return of 37.7% (peaking at 51%), thereby validating a Hopf bifurcation exponent α ≈ 1/2 and demonstrating that linear price impact cannot generate these cycles.
📝 Abstract
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.