  Much of the literature on rational cryptography focuses on analyzing the
strategic properties of cryptographic protocols. However, due to the presence
of computationally-bounded players and the asymptotic nature of cryptographic
security, a definition of sequential rationality for this setting has thus far
eluded researchers.
  We propose a new framework for overcoming these obstacles, and provide the
first definitions of computational solution concepts that guarantee sequential
rationality. We argue that natural computational variants of subgame perfection
are too strong for cryptographic protocols. As an alternative, we introduce a
weakening called threat-free Nash equilibrium that is more permissive but still
eliminates the undesirable ``empty threats'' of non-sequential solution
concepts.
  To demonstrate the applicability of our framework, we revisit the problem of
implementing a mediator for correlated equilibria (Dodis-Halevi-Rabin,
Crypto'00), and propose a variant of their protocol that is sequentially
rational for a non-trivial class of correlated equilibria. Our treatment
provides a better understanding of the conditions under which mediators in a
correlated equilibrium can be replaced by a stable protocol.
