Agentic Limit Order Books: Phase Transitions and Market Impact

Jan Rosenzweig

q-fin.TRSep 25, 2026

Agentic Limit Order Books: Phase Transitions and Market Impact

Authors: Jan Rosenzweig

Abstract

We investigate the systemic macroscopic dynamics emerging from Limit Order Books (LOBs) populated exclusively by autonomous reinforcement-learning agentic traders. By formalizing agent interactions within a microscopic order-matching engine, we examine two fundamental quantitative phenomena: equilibrium phase transitions in order flow regime shifts, and the structural dynamics of market impact. We show that agentic LOBs exhibit distinct phase boundaries separating orderly price discovery from hyper-volatile cascade states, governed by critical thresholds in the number of agents and observable market depth. Furthermore, we demonstrate that market impact under agentic liquidity provision deviates from classical square-root dynamics, exhibiting distinct dissipative, balanced, and non-dissipative regimes under non-linear feedback loops.

Figures & tables

Panel of Figure 1 — Figure 1: Evolution of the Order Book in the Solid (left), Liquid (centre) and Vapour (right) Phases. Positive quantities denote Bids, negative quantities denote Asks, Mid Price is shown in black.

Panel of Figure 2 — Figure 2: Mid-price volatility $\sigma$ and probability of order book collapse $p$ across varying Liquidity Provider count $n$ and Market Depth $d$ . System configuration: 1 Market Agent (Max Qty = 50, frequency = 1 trade/callback), $n$ Liquidity Providers (Max Qty = 50), and $\max(3,\lfloor n/3\rfloor)$ Scalpers (Max Qty = 10).

Phase	Control Parameters ( $n,d$ )	Market State
Collapsed Order Book	$n<n_{c}$	Cascade / Breakdown
Continuous Liquidity	$n>n_{c},\ d>d_{c}(n)$	Stable / Efficient Price Discovery
Frozen Order Book	$d<d_{c}(n)$	Illiquid / Stalled Price Discovery

Table 1: System Regimes in Agentic Limit Order Books

Panel of Figure 3 — Figure 3: Impact and dissipation in the Continuous Phase: First 100 impacted (green) vs. non-impacted (purple) price paths, alongside resulting $z$ -scores.

Panel of Figure 4 — Figure 4: Impact and dissipation in the Frozen Phase: First 100 impacted (green) vs. non-impacted (purple) price paths, alongside resulting $z$ -scores.

Limit Order Book Modeling

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LOB-Impact Benchmark: Emergent Market Impact in Generative Limit Order Book Models

George Nigmatulin, Valentin Mohl, Sascha Frey, Kang Li+5

British Open-ended Learning and Discovery Lab (BOLD), Department of Engineering Science, University of Oxford, Oxford, United Kingdom · British Open-ended Learning and Discovery Lab (BOLD), Department of Computer Science, University of Oxford, Oxford, United Kingdom · British Open-ended Learning and Discovery Lab (BOLD), Department of Statistics, University of Oxford, Oxford, United Kingdom+2

Limit Order Book Modeling Generative Modeling Algorithmic Trading

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Realistic market impact is essential for generative limit order book (LOB) models to serve as world models for trading agents. If a simulator misprices this mechanism, agents learn policies that are optimal in the simulator but wrong in the real market. Existing metrics assess generated streams purely through distributional comparison with historical data, leaving counterfactual response to an agent's own orders largely unexplored. Here, we show that market impact emerges naturally in neural LOB generators trained solely for next-token prediction. We inject execution-style metaorders into the generated message flow of five autoregressive models across five NASDAQ stocks and measure the response using estimators from the empirical impact literature, validated on baselines whose physics is known in advance. Our benchmark evaluates any message-level generator in three phases: free generation (reading order-flow persistence against price diffusivity); metaorder injection (yielding the impact law's exponent and amplitude); and a post-execution window (measuring relaxation). In addition, comparing each visible injection to a blind, simulator-only control isolates the model's learned response from standard book mechanics. For every model on every stock, we measure how the impact responds as a function of cumulative metaorder participation. Interestingly, we observe emergent impact in generative models of market data, with exponents in the range of 0.63 to 1.21, slightly above the traditional 0.5 of the square-root law of impact. In the family of models tested, we are so far unable to observe impact decay during relaxation. We tentatively attribute this to the still-short context windows of the models. We release the benchmark as open source to validate future generative models for market data.

Abstract

Limit Order Book Modeling

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