Regulatory changes are transforming the multitrillion dollar swaps market from a network of bilateral contracts to one in which swaps are cleared through central counterparties (CCPs). The stability of the new framework depends on the CCPs’ resilience. Margin requirements are a CCP’s first line of defense against the default of a counterparty. To capture liquidity costs at default, margin requirements need to increase superlinearly in position size. However, convex margin requirements create an incentive for a swaps dealer to split its positions across multiple CCPs, effectively “hiding” potential liquidation costs from each CCP. To compensate, each CCP needs to set higher margin requirements than it would in isolation. In a model with two CCPs, we define an equilibrium as a pair of margin schedules through which both CCPs collect sufficient margin under a dealer’s optimal allocation of trades. In the case of linear price impact, we show that a necessary and sufficient condition for the existence of an equilibrium is that the two CCPs agree on liquidity costs, and we characterize all equilibria when this holds. A difference in views can lead to a race to the bottom. We provide extensions of this result and discuss its implications for CCP oversight and risk management.