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The fair exchange problem is key to trading electronic items in systems of mutually untrusted parties. In modern variants of such systems, each party is equipped with a security module. The security modules trust each other but can only communicate by exchanging messages through their untrusted host parties,that could drop those messages. We describe a synchronous algorithm that ensures deterministic fair exchange if a majority of parties are honest, which is optimal in terms of resilience. If there is no honest majority, our algorithm degrades gracefully: it ensures that the probability of unfairness can be made arbitrarily low. Our algorithm uses, as an underlying building block, an early-stopping subprotocol that solves, in a general omission failure model, a specific variant of consensus we call biased consensus. Interestingly, this modular approach combines concepts from both cryptography and distributed computing, to derive new results on the classical fair exchange problem.