Square-Root Price Impact Is Necessary for Endogenous Manipulation Cycles in Learning-Agent Markets
Key Insights
- 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 preda.
Show formatted citation
@misc{ acaciaaml-research-square-root-price-impact-is-necessary-for-endogenous-manipul,
title = { Square-Root Price Impact Is Necessary for Endogenous Manipulation Cycles in Learning-Agent Markets },
author = { Leszek },
year = { 2026 },
doi = { 10.48550/arXiv.2607.05141 },
url = { http://arxiv.org/abs/2607.05141v1 },
note = {Summarized and classified by AcaciaFund}
}
TY - GEN TI - Square-Root Price Impact Is Necessary for Endogenous Manipulation Cycles in Learning-Agent Markets AU - Leszek PY - 2026 DO - 10.48550/arXiv.2607.05141 UR - http://arxiv.org/abs/2607.05141v1 ER -
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Overview
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 pattern: it learns to move the market, harvest the crowd's predictable reaction, and repeat the cycle.
The Setup
The institutional agent's behavior is not hand-coded by the authors; it is the outcome of an evolutionary optimization loop. The retail population follows a herding rule, so its behavior is simple and deterministic. The interesting result is what the optimizer finds: a strategy that exploits the crowd's inertia across repeated rounds rather than a one-off manipulation.
The Key Finding
The paper's central result is structural: the emergence and stability of these manipulation cycles requires a square-root price impact function. Under that shape of market impact, the predator's own trading moves prices enough to mislead the herd, the herd's reaction creates the predictable next move, and the cycle can repeat endogenously — no external news is required to keep it alive.
Why It Matters
For market surveillance and AML teams the paper is a model-building lesson: endogenous manipulation cycles can exist even in a minimal, fully specified market, and their existence depends on the market's impact function, not on the predator's sophistication alone. Impact-curve assumptions should be part of any agent-based market-abuse experiment, because they determine whether manipulation is a transient artifact or a stable equilibrium.
Key Takeaways
- Manipulation can be learned, not designed — evolutionary optimization discovers predation patterns nobody specified.
- Square-root impact is the load-bearing assumption; other impact shapes destroy the cycle.
- Surveillance models should stress-test for endogenous cycles driven purely by feedback between informed and herding traders.