Abstract

We study stablecoin peg stability as the equilibrium outcome of a Stackelberg game between stablecoin issuer and arbitrageurs. The issuer chooses the stablecoin supply policy, while the arbitrageur allocates capital to peg arbitrage subject to downside risk. Peg deviations are driven by supply imbalances relative to a benchmark demand-driven supply but are diminished by endogenous market depth provided by arbitrage capital. We derive a closed-form arbitrageur optimal response under CARA preferences with a participation threshold, generating an endogenous no-arbitrage zone in price space. Outside this zone, arbitrage increases with imbalances but can be self-limiting when downside risk rises faster than expected profits. Anticipating this response, the issuer optimally adjusts its supply toolkit via a threshold rule, trading off issuance incentives against peg penalties under limited arbitrage. We outline a calibration using MakerDAO DAI data.