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arxiv: 2601.18991 · v2 · submitted 2026-01-26 · 💱 q-fin.TR · cs.GT· econ.GN· q-fin.EC

Who Restores the Peg? A Mean-Field Game Approach to Model Stablecoin Market Dynamics

Hardhik Mohanty , Bhaskar Krishnamachari This is my paper

Pith reviewed 2026-05-16 10:32 UTC · model grok-4.3

classification 💱 q-fin.TR cs.GTecon.GNq-fin.EC
keywords stablecoinsde-peggingmean-field gamesarbitragemarket dynamicspeg restorationUSDCUSDT
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The pith

Primary-market arbitrage restores the peg in a mean-field game model of stablecoin dynamics

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

The paper develops a mean-field game model for stablecoin de-pegging events involving arbitrageurs and retail traders in primary and secondary markets. This framework endogenously determines price paths and order flows from market frictions, enabling attribution of who stabilizes the peg. Calibration to three historical events shows the model matches observed recovery times and indicates that primary-market arbitrage provides most of the stabilizing pressure. A sensitivity analysis reveals a non-linear threshold where de-pegs become much harder to reverse.

Core claim

We develop a dynamic, agent-based mean-field game framework for fiat-collateralized stablecoins in which arbitrageurs and retail traders strategically interact across primary and secondary markets during a de-peg episode. The equilibrium formulation maps market frictions into a market-clearing price path and implied net order flows, allowing attribution of peg-reverting pressure by channel. Using three historical de-peg events, the calibrated equilibrium reproduces observed recovery half-lives and shows system-wide stress is predominantly stabilized by primary-market arbitrage. A quantitative sensitivity analysis identifies a non-linear breakdown threshold beyond which a de-peg becomes-markd

What carries the argument

The mean-field game equilibrium that endogenously determines the market-clearing price path and net order flows from strategic interactions of agents facing market frictions.

Load-bearing premise

The mean-field equilibrium and friction parameters calibrated to three events continue to describe out-of-sample de-peg behavior, with primary and secondary market flows cleanly separable in the data.

What would settle it

Observing a new de-peg event where the recovery half-life differs substantially from the model's prediction or where secondary-market flows dominate the order flow decomposition.

Figures

Figures reproduced from arXiv: 2601.18991 by Bhaskar Krishnamachari, Hardhik Mohanty.

Figure 1
Figure 1. Figure 1: Market structure for fiat-collateralized stablecoins. The [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the Mean-Field Game (MFG) framework [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of the simulated stablecoin price path against the historical observed price data during each de-peg event. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Calibrated model parameters across three distinct market regimes identified during each de-peg event. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Historical price trajectories and estimated AR(1) half [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Decomposition of net peg-reverting flows into primary-market mint/redeem flow and secondary-market buying flow on [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: De-peg half-life sensitivity to market frictions [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: De-peg half-life as a function of retail trader share [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Convergence diagnostics and coupling sensitivity. Left: exploitability [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
read the original abstract

USDC and USDT are the dominant stablecoins pegged to \$1 with a total market capitalization of over \$300B and rising. Stablecoins make dollar value globally accessible with secure transfer and settlement. Yet in practice, these stablecoins experience periods of stress and de-pegging from their \$1 target, posing significant systemic risks. The behavior of market participants during these stress events and the collective actions that either restore or break the peg are not well understood. This paper addresses the question: who restores the peg?. We develop a dynamic, agent-based mean-field game framework for fiat-collateralized stablecoins, in which a large population of arbitrageurs and retail traders strategically interact across primary and secondary markets during a de-peg episode. The key advantage of this equilibrium formulation is that it endogenously maps market frictions into a market-clearing price path and implied net order flows, allowing us to attribute peg-reverting pressure by channel and to stress-test when a given infrastructure becomes insufficient for recovery. Using three historical de-peg events, we show that the calibrated equilibrium reproduces observed recovery half-lives and yields an order flow decomposition in which system-wide stress is predominantly stabilized by primary-market arbitrage. Finally, a quantitative sensitivity analysis identifies a non-linear breakdown threshold, beyond which a de-peg becomes markedly slower to reverse.

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.

Referee Report

3 major / 2 minor

Summary. The paper develops a dynamic mean-field game framework for fiat-collateralized stablecoins in which arbitrageurs and retail traders interact strategically across primary and secondary markets during de-peg episodes. The equilibrium endogenously determines a market-clearing price path and net order flows from market frictions. Calibrated to three historical de-peg events, the model reproduces observed recovery half-lives and decomposes order flows to conclude that primary-market arbitrage supplies the dominant restoring pressure; a sensitivity analysis identifies a nonlinear breakdown threshold beyond which recovery slows markedly.

Significance. If the primary-market attribution and breakdown threshold prove robust, the framework would offer a useful quantitative tool for attributing stabilization channels and stress-testing stablecoin infrastructure. The endogenous mapping from frictions to flows is a conceptual strength, but the current calibration-to-validation design on the same three events limits the strength of the decomposition claim.

major comments (3)
  1. [§4] §4 (Calibration and Results): The friction and cost parameters are fitted to the identical three de-peg episodes whose half-lives are subsequently reported as reproduced. Because the equilibrium map from these parameters to price paths and net flows is continuous, any event-specific features absorbed in calibration will be attributed to the channel labeled “primary-market arbitrage,” undermining the claim that the decomposition is structural rather than fitted.
  2. [§5] §5 (Sensitivity Analysis): The reported nonlinear breakdown threshold is obtained from the same calibrated parameter set; without a hold-out event or parameter-stability check across additional episodes, it is unclear whether the threshold reflects a genuine market feature or an artifact of the three-event sample.
  3. [Abstract, §3] Abstract and §3 (Model): The abstract states that the equilibrium “yields an order flow decomposition in which system-wide stress is predominantly stabilized by primary-market arbitrage,” yet no out-of-sample test or cross-validation procedure is described to separate this attribution from the calibration procedure itself.
minor comments (2)
  1. [§3] Notation for the mean-field distribution and the distinction between primary- and secondary-market flows should be introduced earlier and used consistently; several equations in §3 reuse symbols without redefinition.
  2. [Figures 2-4] Figure captions for the price-path and flow-decomposition plots should explicitly state the data sources and any filtering rules applied to the three events.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below, acknowledging the calibration limitations while defending the structural role of the equilibrium. We propose targeted revisions to qualify claims and add robustness checks.

read point-by-point responses

  1. Referee: [§4] The friction and cost parameters are fitted to the identical three de-peg episodes whose half-lives are subsequently reported as reproduced. Because the equilibrium map from these parameters to price paths and net flows is continuous, any event-specific features absorbed in calibration will be attributed to the channel labeled “primary-market arbitrage,” undermining the claim that the decomposition is structural rather than fitted.

    Authors: We agree that using the same three events for calibration and reported reproduction limits out-of-sample strength. However, the mean-field game imposes optimality conditions and market-clearing constraints that restrict the admissible mappings from parameters to flows, providing identification beyond arbitrary fitting. In revision we will expand §4 with an explicit identification discussion, report decomposition results under leave-one-event-out recalibrations, and qualify the primary-market attribution as holding in the calibrated equilibria for these episodes. revision: partial

  2. Referee: [§5] The reported nonlinear breakdown threshold is obtained from the same calibrated parameter set; without a hold-out event or parameter-stability check across additional episodes, it is unclear whether the threshold reflects a genuine market feature or an artifact of the three-event sample.

    Authors: We acknowledge the sample-size concern. The revised §5 will include a parameter-stability exercise that perturbs calibrated values within bootstrap confidence intervals, recomputes the breakdown threshold, and reports the range of thresholds obtained. We will also add text noting that the nonlinearity is a feature of the calibrated model and that broader validation requires additional de-peg episodes. revision: yes

  3. Referee: [Abstract, §3] The abstract states that the equilibrium “yields an order flow decomposition in which system-wide stress is predominantly stabilized by primary-market arbitrage,” yet no out-of-sample test or cross-validation procedure is described to separate this attribution from the calibration procedure itself.

    Authors: We will revise the abstract to read that the calibrated equilibrium suggests primary-market arbitrage supplies the dominant restoring pressure. In §3 we will insert a short paragraph clarifying that the decomposition is structural within the equilibrium but that quantitative attribution relies on calibration to the observed episodes, thereby aligning wording with the methodology. revision: yes

Circularity Check

1 steps flagged

Calibration to three de-peg events makes reproduction of half-lives and order-flow decomposition tautological by construction

specific steps
  1. fitted input called prediction [Abstract]
    "Using three historical de-peg events, we show that the calibrated equilibrium reproduces observed recovery half-lives and yields an order flow decomposition in which system-wide stress is predominantly stabilized by primary-market arbitrage."

    Parameters (transaction costs, inventory penalties, etc.) are fitted to the three events; the equilibrium is then shown to reproduce the half-lives and flows from those identical events. The reproduction and decomposition are therefore outputs of the same fitting procedure, not independent predictions.

full rationale

The central empirical result calibrates friction parameters of the mean-field game to three historical events and then reports that the resulting equilibrium reproduces the observed recovery half-lives of those same events while decomposing order flows. Because the equilibrium price path and net flows are continuous functions of the fitted parameters, any match to the calibration targets is guaranteed by construction rather than an independent test. The attribution of stabilization to primary-market arbitrage therefore inherits the same dependence on the three-event sample. No parameter-free prediction, hold-out validation, or external benchmark is indicated in the abstract or skeptic summary.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on a mean-field approximation for strategic interaction and on parameters calibrated to historical de-peg data; no new entities are postulated.

free parameters (1)
  • friction and cost parameters
    Calibrated to match observed recovery half-lives in the three historical events.
axioms (1)
  • domain assumption Mean-field limit for large population of agents
    Invoked to obtain tractable equilibrium price paths from individual optimization.

pith-pipeline@v0.9.0 · 5552 in / 1265 out tokens · 46855 ms · 2026-05-16T10:32:16.250924+00:00 · methodology

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Reference graph

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