  We consider the problem of cross-chain payment whereby customers of different
escrows---implemented by a bank or a blockchain smart contract---successfully
transfer digital assets without trusting each other. Prior to this work,
cross-chain payment problems did not require this success, or any form of
progress. We demonstrate that it is possible to solve this problem when
assuming synchrony, in the sense that each message is guaranteed to arrive
within a known amount of time, but impossible to solve without assuming
synchrony. Yet, we solve a weaker variant of this problem, where success is
conditional on the patience of the participants, without assuming synchrony,
and in the presence of Byzantine failures. We also discuss the relation with
the recently defined cross-chain deals.
