arxiv: 2604.20067 · v1 · submitted 2026-04-22 · 💱 q-fin.TR

Recognition: unknown

Testing replication for an agent-based model of market fragmentation and latency arbitrage

Brian F. Tivnan, Colin M. Van Oort, Ethan Ratliff-Crain, Matthew T. K. Koehler

Pith reviewed 2026-05-09 23:06 UTC · model grok-4.3

classification 💱 q-fin.TR

keywords replicationagent-based modelingmarket fragmentationlatency arbitragezero-intelligence tradersgreedy strategysimulation robustness

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The pith

A replication of the 2016 market fragmentation model finds that its main qualitative results reverse when the zero-intelligence traders use an alternative version of the greedy strategy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper attempts an independent replication of Wah and Wellman's agent-based model of latency arbitrage across multiple trading venues. Missing details in the original description and limited quantitative reporting make exact reproduction difficult, so the authors increase the number of simulation runs to generate bootstrap confidence intervals and enable formal tests of alignment. They recover extra implementation information from a later code release but still reject quantitative matches for any setting with non-zero latency. Most metrics show relational equivalence, yet the original conclusions about fragmentation harming trader welfare and lengthening execution times depend on one specific reading of the greedy strategy extension to the zero-intelligence agents. Under a different reading of that same strategy, fragmentation shortens execution times in every experiment and raises welfare in most of them.

Core claim

The central claim is that many qualitative takeaways from the original model are sensitive to the precise implementation of the greedy strategy given to zero-intelligence trader agents. When the authors substitute an alternative interpretation of that strategy, market fragmentation decreases execution times across all experiments and increases trader welfare in most experiments, while the original results do not hold.

What carries the argument

The zero-intelligence trader agents equipped with a greedy strategy extension, whose exact decision rule determines whether fragmentation improves or worsens execution speed and welfare.

If this is right

More simulation runs allow bootstrap confidence intervals that support statistical tests of quantitative alignment in agent-based market models.
Relational equivalence can be achieved even when quantitative alignment fails in higher-complexity latency settings.
Releasing an ODD protocol alongside code makes future independent replications and extensions of the model easier to perform.
Qualitative policy conclusions about market structure can change when the same agent rule is implemented in a different but still plausible way.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Finance simulation studies may need explicit decision-rule variants documented at publication to avoid hidden sensitivity in reported outcomes.
Regulators or exchange designers using such models should test multiple reasonable interpretations of trader behavior before acting on fragmentation effects.
The bootstrap-interval method demonstrated here could be applied to other published agent-based studies that report only mean outcomes without variance data.

Load-bearing premise

The alternative interpretation of the greedy strategy counts as a fair robustness check on the original model rather than a material change to its intent, and relational equivalence on most metrics is enough to establish qualitative sensitivity even when quantitative alignment is rejected.

What would settle it

Running the released original codebase and the new replication side-by-side with identical random seeds, parameter values, and the two different greedy-strategy rules would show whether the reported reversal in execution times and welfare is reproduced or disappears.

Figures

Figures reproduced from arXiv: 2604.20067 by Brian F. Tivnan, Colin M. Van Oort, Ethan Ratliff-Crain, Matthew T. K. Koehler.

**Figure 2.** Figure 2: Visualization of WW following the vODD format [ [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Mean surplus results from our implementations of the model and [PITH_FULL_IMAGE:figures/full_fig_p025_3.png] view at source ↗

**Figure 4.** Figure 4: Mean execution time results from our implementations of the model and [PITH_FULL_IMAGE:figures/full_fig_p026_4.png] view at source ↗

**Figure 5.** Figure 5: Mean median spreads from the exchange BBOs for our implementations of the model and [PITH_FULL_IMAGE:figures/full_fig_p027_5.png] view at source ↗

**Figure 6.** Figure 6: Mean median SIP NBBO spread for our implementations of the model and [PITH_FULL_IMAGE:figures/full_fig_p028_6.png] view at source ↗

**Figure 7.** Figure 7: Mean number of transactions from our implementations of the model and [PITH_FULL_IMAGE:figures/full_fig_p029_7.png] view at source ↗

**Figure 8.** Figure 8: Execution time and spread results from our [PITH_FULL_IMAGE:figures/full_fig_p037_8.png] view at source ↗

**Figure 9.** Figure 9: ZI order routing logic from MarketSim (https://github.com/egtaonline/market-sim/ blob/marketsim1/hft-sim/src/entity/market/Market.java#L471). Note that the code first checks that quantity is greater than zero, then uses whether quantity is greater than zero to determine whether the order is to buy or sell the asset. Thus, all orders will enter the ‘buy’ block, thus being routed based on the best ask price… view at source ↗

**Figure 10.** Figure 10: Mean surplus results from our BestGuess+MS and BestGuess+MS+bug implementations of the model. These results should be compared to the corresponding original figures from WW [57] ( [PITH_FULL_IMAGE:figures/full_fig_p039_10.png] view at source ↗

**Figure 11.** Figure 11: Mean execution time results from our BestGuess+MS and BestGuess+MS+bug implementations of the model. These results should be compared to the corresponding original figures from WW [57] ( [PITH_FULL_IMAGE:figures/full_fig_p040_11.png] view at source ↗

**Figure 12.** Figure 12: Mean median spreads from the exchange BBOs for our [PITH_FULL_IMAGE:figures/full_fig_p040_12.png] view at source ↗

**Figure 13.** Figure 13: Mean median SIP NBBO spread for our BestGuess+MS and BestGuess+MS+bug implementations of the model versus the figures reproduced from WW [57] ( [PITH_FULL_IMAGE:figures/full_fig_p041_13.png] view at source ↗

**Figure 14.** Figure 14: Mean number of transactions from our BestGuess+MS and BestGuess+MS+bug implementations of the model. These results should be compared to the corresponding original figures from WW [57] ( [PITH_FULL_IMAGE:figures/full_fig_p041_14.png] view at source ↗

read the original abstract

This study strengthens the foundations of multi-venue market modeling by attempting an independent replication of Wah and Wellman's 2016 model of latency arbitrage in a fragmented market. We find that faithful replication is hindered by missing implementation details in the original paper and limited quantitative reporting. We demonstrate that increasing the number of simulation runs beyond the original design allows for the creation of bootstrap confidence intervals to support rigorous tests of quantitative alignment, compensating for lacking distributional information (e.g. variance). We also demonstrate that increased complexity across the modeled scenarios corresponds with increased difficulty aligning to the original results. We draw on a codebase released by the original authors in connection with a later paper to recover additional implementation details; however, we reject quantitative alignment between that codebase and the published results. Combining information from the paper and the released code, we achieve relational equivalence for most metrics but reject quantitative alignment for model settings where latency is non-zero. We show that many of the qualitative takeaways from the original paper on the effects of market fragmentation and latency arbitrage are sensitive to the specifics of a `greedy strategy' extension given to the zero-intelligence (ZI) trader agents. Under an alternative interpretation of this strategy, we find that market fragmentation decreases execution times in all experiments and increases trader welfare in most experiments. Finally, to facilitate future replication, critique, and extension, we provide an ODD (Overview, Design concepts, Details) protocol for our implementations of the model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The replication is careful and the ODD protocol is useful, but the claim that qualitative results flip under an alternative greedy strategy rests on an unverified interpretation that may not match the original model intent.

read the letter

The main point is that this replication finds the original Wah and Wellman conclusions on market fragmentation and latency arbitrage are sensitive to the greedy strategy extension for zero-intelligence traders. Under the authors' alternative version, fragmentation cuts execution times in every experiment and raises trader welfare in most of them, reversing some earlier takeaways. They also reject quantitative alignment with both the published results and the released code once latency is non-zero. That is the headline result worth noting. They do the replication work properly. Bootstrap confidence intervals and relational equivalence checks add real rigor where the original paper gave only point estimates. Pulling details from the later codebase release is transparent, and the ODD protocol they supply will help anyone who wants to re-run or extend the model. Those are concrete advances for reproducibility in this corner of computational finance. The soft spot is the sensitivity claim itself. The paper shows they cannot align quantitatively on the non-zero latency settings, yet the reversal depends on treating their alternative greedy strategy as a minor robustness check. No direct mapping or quoted decision rule from the 2016 description is given to show why this version is close enough to the original intent rather than a change in order placement or cancellation logic. Without that, the flip could reflect implementation differences instead of fragility in the base model. This paper is for researchers who build or replicate agent-based market models and for anyone tracking reproducibility standards in the field. A reader focused on those issues will find the statistical approach and protocol worth the time. It deserves a serious referee because it surfaces genuine documentation gaps and offers a workable way to test alignment, even if the central sensitivity argument needs tighter grounding on the strategy choice.

Referee Report

2 major / 2 minor

Summary. The manuscript is an independent replication study of Wah and Wellman (2016) on an agent-based model of market fragmentation and latency arbitrage. It reports that faithful replication is impeded by missing implementation details and limited quantitative reporting in the original; the authors combine the paper with a later-released codebase, introduce bootstrap confidence intervals for alignment tests, achieve relational equivalence on most metrics while rejecting quantitative alignment for non-zero latency, and show that qualitative conclusions on fragmentation and latency-arbitrage effects are sensitive to the interpretation of the 'greedy strategy' extension to zero-intelligence traders. Under an alternative reading of that strategy, fragmentation reduces execution times in all experiments and raises trader welfare in most. An ODD protocol is supplied to support future work.

Significance. If the sensitivity result is robust, the work usefully illustrates how underspecified agent rules in ABMs can affect policy-relevant conclusions about market design, while the bootstrap-CI and relational-equivalence methods, together with the ODD protocol, supply concrete tools that strengthen replicability standards in quantitative finance. The explicit release of implementation details is a clear positive contribution.

major comments (2)

[§5] §5 (alternative greedy-strategy results): The central claim that 'many of the qualitative takeaways ... are sensitive to the specifics of a greedy strategy extension' rests on comparing the authors' recovered implementation against an alternative interpretation. Because quantitative alignment is rejected for non-zero latency (both with the published results and the released codebase), the manuscript must demonstrate that the alternative is a minor clarification rather than a substantive change to order-placement or cancellation logic. No direct quotation or formal alignment to the original Wah & Wellman (2016) description is provided, so the observed reversal (fragmentation always lowers execution time, mostly improves welfare) could be an artifact of the chosen alternative rather than evidence of fragility in the original model.
[Methods] Methods (relational-equivalence definition): The paper adopts relational equivalence as a proxy when quantitative matches cannot be achieved, citing an ad-hoc axiom that this is valid. Given that the sensitivity conclusion depends on this proxy, the decision procedure used to construct the alternative greedy strategy must be stated explicitly and shown to be independent of the authors' own implementation choices; otherwise the test does not isolate sensitivity of the original model.

minor comments (2)

[Abstract] Abstract: the phrase 'many of the qualitative takeaways' is left unspecified; a short list of the affected metrics (execution time, welfare, etc.) would improve precision.
[Tables and figures] Table/figure captions: several metric definitions (e.g., exact welfare calculation, execution-time aggregation) are referenced but not restated; a compact notation table would aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped clarify how to strengthen the presentation of our replication results. We address each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

Referee: [§5] §5 (alternative greedy-strategy results): The central claim that 'many of the qualitative takeaways ... are sensitive to the specifics of a greedy strategy extension' rests on comparing the authors' recovered implementation against an alternative interpretation. Because quantitative alignment is rejected for non-zero latency (both with the published results and the released codebase), the manuscript must demonstrate that the alternative is a minor clarification rather than a substantive change to order-placement or cancellation logic. No direct quotation or formal alignment to the original Wah & Wellman (2016) description is provided, so the observed reversal (fragmentation always lowers execution time, mostly improves welfare) could be an artifact of the chosen alternative rather than evidence of fragility in the original model.

Authors: We agree that direct quotations and explicit alignment to the original description are necessary. In the revised manuscript we now include verbatim excerpts from Wah and Wellman (2016) on the greedy extension to ZI traders. The original wording is brief and leaves the precise scope of 'greedy' (venue selection for placement versus cancellation) ambiguous. Our alternative reading is constructed as one logically consistent interpretation of that ambiguity while preserving the zero-intelligence character of the agents. We have added a side-by-side comparison table that maps each interpretation to the original text, showing that the difference is confined to the scope of the greedy rule rather than a change in order-placement or cancellation mechanics. This addition supports our claim that the qualitative reversal illustrates sensitivity to underspecification rather than constituting an artifact. revision: yes
Referee: [Methods] Methods (relational-equivalence definition): The paper adopts relational equivalence as a proxy when quantitative matches cannot be achieved, citing an ad-hoc axiom that this is valid. Given that the sensitivity conclusion depends on this proxy, the decision procedure used to construct the alternative greedy strategy must be stated explicitly and shown to be independent of the authors' own implementation choices; otherwise the test does not isolate sensitivity of the original model.

Authors: We have revised the Methods section to provide an explicit, step-by-step decision procedure for constructing the alternative greedy strategy. The procedure is: (1) extract every sentence in Wah and Wellman (2016) that describes ZI trader behavior and the greedy extension; (2) flag all points of ambiguity in how 'greedy' is applied; (3) enumerate interpretations that remain consistent with zero-intelligence principles (no lookahead or global optimization); and (4) adopt the reading that differs from the recovered implementation only in the scope of the greedy choice. This procedure was derived exclusively from the published paper text before any code inspection or modification, thereby ensuring independence from our implementation choices. We also clarify that relational equivalence is used only where quantitative alignment is impossible due to missing variance statistics in the original work, and we rely on bootstrap confidence intervals for the statistical tests. revision: yes

Circularity Check

0 steps flagged

Replication uses external benchmarks and independent re-implementation with no reduction to self-fitted inputs

full rationale

The paper is a replication study of Wah & Wellman (2016). It compares an independent re-implementation against the original published results and a separately released codebase from the original authors' later work. Quantitative alignment is explicitly rejected for non-zero latency settings, and relational equivalence is reported only after combining external sources. The sensitivity claim on the greedy ZI strategy rests on an explicit alternative interpretation whose results are contrasted with the recovered implementation; no parameter is fitted from the present paper's own outputs and then renamed as a prediction. No self-citations are load-bearing, no uniqueness theorems are imported from the authors' prior work, and no ansatz or renaming of known results occurs. The ODD protocol is supplied to make the implementation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that zero-intelligence traders can be extended with a greedy strategy whose precise form is ambiguous in the original work, plus the modeling choice that relational equivalence suffices when exact numerical matches fail.

axioms (2)

domain assumption Zero-intelligence traders operate with a greedy strategy extension whose implementation details are not fully specified in the original paper
Invoked when testing sensitivity of qualitative results to alternative interpretations of the strategy.
ad hoc to paper Relational equivalence on metrics is a valid proxy for model alignment when quantitative matches cannot be achieved due to missing original details
Used to support claims despite rejected quantitative alignment for non-zero latency.

pith-pipeline@v0.9.0 · 5574 in / 1510 out tokens · 58075 ms · 2026-05-09T23:06:23.829108+00:00 · methodology

discussion (0)

Reference graph

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Jan C Thiele and Volker Grimm. Replicating and breaking models: good for you and good for ecology.Oikos, 124(6):691–696, 2015. Publisher: Wiley Online Library

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Adding to the Regulator’s Toolbox: Integration and Extension of Two Leading Market Models.Papers, May 2011

Brian Tivnan, Matthew Koehler, Matthew McMahon, Matthew Olson, Neal Rothleder, and Ra- jani Shenoy. Adding to the Regulator’s Toolbox: Integration and Extension of Two Leading Market Models.Papers, May 2011

2011
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Tivnan, Matthew T

Brian F. Tivnan, Matthew T. K. Koehler, David Slater, Jason Veneman, and Brendan F. Tivnan. Towards a model of the U.S. stock market: How important is the securities information processor? In2017 Winter Simulation Conference (WSC), pages 1181–1192, December 2017

2017
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Securities and Exchange Commission

U.S. Securities and Exchange Commission. Regulation NMS. Technical Report Release No. 34- 51808, U.S. Securities and Exchange Commission, 2005

2005
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Securities and Exchange Commission

U.S. Securities and Exchange Commission. Regulation NMS: Minimum Pricing Increments, Access Fees, and Transparency of Better Priced Orders. Technical Report Release No. 34-101070, U.S. Securities and Exchange Commission, 2024

2024
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Adaptive Agents and Data Quality in Agent-Based Financial Markets.arXiv preprint arXiv:2311.15974, 2023

Colin M Van Oort, Ethan Ratliff-Crain, Brian F Tivnan, and Safwan Wshah. Adaptive Agents and Data Quality in Agent-Based Financial Markets.arXiv preprint arXiv:2311.15974, 2023

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Wouter Vermeer, Arthur Hjorth, Samuel M Jenness, Hendrick Brown, and Uri Wilensky. Leverag- ing modularity during replication of high-fidelity models: lessons from replicating an agent-based model for HIV prevention.Journal of artificial societies and social simulation: JASSS, 23(4):7, 2020

2020
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Christian E Vincenot. How new concepts become universal scientific approaches: insights from citation network analysis of agent-based complex systems science.Proceedings of the Royal Society B: Biological Sciences, 285(1874):20172360, 2018. Publisher: The Royal Society

2018
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Elaine Wah.Computational Models of Algorithmic Trading in Financial Markets.PhD Thesis, 2016

2016
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Latency arbitrage, market fragmentation, and efficiency: A two-market model

Elaine Wah and Michael P Wellman. Latency arbitrage, market fragmentation, and efficiency: A two-market model. InProceedings of the fourteenth ACM conference on Electronic commerce, pages 855–872, 2013. ©2026 The MITRE Corporation. ALL RIGHTS RESER VED. Approved for Public Release; Distribution Unlimited. Public Release Case Number 25-1956. 34 A USINGMARK...

2013
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Latency arbitrage in fragmented markets: A strategic agent-based analysis.Algorithmic Finance, 5(3-4):69–93, 2016

Elaine Wah and Michael P Wellman. Latency arbitrage in fragmented markets: A strategic agent-based analysis.Algorithmic Finance, 5(3-4):69–93, 2016

2016
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Welfare effects of market making in contin- uous double auctions.Journal of Artificial Intelligence Research, 59:613–650, 2017

Elaine Wah, Mason Wright, and Michael P Wellman. Welfare effects of market making in contin- uous double auctions.Journal of Artificial Intelligence Research, 59:613–650, 2017

2017
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Empirical game theoretic analysis: A survey.Journal of artificial intelligence research, 82:1017–1076, 2025

Michael P Wellman, Karl Tuyls, and Amy Greenwald. Empirical game theoretic analysis: A survey.Journal of artificial intelligence research, 82:1017–1076, 2025

2025
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Making models match: Replicating an agent-based model

Uri Wilensky and William Rand. Making models match: Replicating an agent-based model. Journal of Artificial Societies and Social Simulation, 10(4):2, 2007

2007
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Resolving a replication that failed: News on the Macy & Sato model.Journal of Artificial Societies and Social Simulation, 12(4):11, 2009

Oliver Will. Resolving a replication that failed: News on the Macy & Sato model.Journal of Artificial Societies and Social Simulation, 12(4):11, 2009

2009
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The background traders arrive at the market according to a Poisson process with rateλ

Oliver Will and Rainer Hegselmann. A Replication That Failed on the Computational Model in’Michael W. Macy and Yoshimichi Sato: Trust, Cooperation and Market Formation in the US and Japan. Proceedings of the National Academy of Sciences, May 2002’.Journal of Artificial Societies and Social Simulation, 11(3):3, 2008. A UsingMarketSimto replicate WWW In ord...

2002
[63]

They do not specify how the ZI arrival times are made to be discrete

(p.75). They do not specify how the ZI arrival times are made to be discrete. We draw the ZI arrival times independently from an exponential distribution (⌈Exponential(1/λ)⌉). We choose to take the ceiling such that no event will be scheduled at timet= 0. We account for this by letting arrivals occur on times 1 throughT(inclusive), givingTtotal time steps...

2026
[64]

[E]vents are maintained in a queue ordered by time of occurrence

except forα. Theαvalue is based on the 2013 paper [56] and Wah’s dissertation [55], and it is further confirmed by looking at the default valueαinMarketSim. ID Rmin Rmax η ZI 1 0 125 1 ZI 2 0 250 1 ZI 3 0 500 1 ZI 4 250 500 1 ZI 5 0 1000 1 ZI 6 500 1000 0.4 ZI 7 500 1000 1 ZI 8 0 1500 0.6 ZI 9 1000 2000 0.4 ZI 10 0 2500 0.4 ZI 11 0 2500 1 Table 19: ZI str...

2013
[65]

Orders: map from order IDs to their respective orders
[66]

Bids: map from price to the queue of buy order IDs at that price
[67]

We measure execution time by the interval between order submission and transaction for orders that eventually trade

Asks: map from price to the queue of sell order IDs at that price The exchange publishes a BBO to its subscribers, a feed containing the best bid and offer prices in the LOB at that moment. LOBs are initialized with no bids or asks at the start. The BBO has null prices for its best available bid and ask whenever their respective side of the LOB is empty (...

2026