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

TL;DR

This paper tackles the problem of stablecoin peg maintenance under stress by modeling a dynamic continuum of traders and arbitrageurs who interact across primary mint/redeem rails and secondary venues. It introduces a dynamic mean-field game (MFG) framework where the mean-field state $\mu_t=(m_t,L_t,\phi_t,\psi_t)$ jointly evolves with agent policies, yielding a tractable equilibrium that generates endogenous peg paths and net order flows. Calibrated to three historical de-peg events, the model reproduces observed recovery half-lives and decomposes peg restoration into primary and secondary channels, revealing a non-linear threshold in primary-market friction that governs resilience. The findings have practical implications for stablecoin design and regulation, highlighting the pivotal role of mint/redeem rails and their resilience in peg restoration, beyond mere reserve quality, and offering a framework for counterfactuals and risk management.

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 interacts across explicit primary (mint/redeem) and secondary (exchange) 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 mechanism 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, whereas episodes with impaired primary redemption require a joint recovery via both primary and secondary markets. Finally, a quantitative sensitivity analysis of primary-rail frictions identifies a non-linear breakdown threshold. Beyond this point, secondary-market liquidity acts mainly as a second-order amplifier around this primary-market bottleneck.

Figures (9)

• Figure 1: Market structure for fiat-collateralized stablecoins. The primary market involves the treasury and arbitrageurs for 1:1 minting and redeeming, while the secondary market includes exchanges and retail traders for buying and selling.
• Figure 2: Overview of the Mean-Field Game (MFG) framework used to model agent dynamics for stablecoin markets.
• Figure 3: Comparison of the simulated stablecoin price path against the historical observed price data during each de-peg event.
• Figure 4: Calibrated model parameters across three distinct market regimes identified during each de-peg event.
• Figure 5: Historical price trajectories and estimated AR(1) half-lives for the three de-peg events.