Sequential Rationality in Cryptographic Protocols

TL;DR

This paper introduces a new framework for defining sequential rationality in cryptographic protocols with computationally bounded players, using threat-free Nash equilibrium to ensure stability and eliminate empty threats.

Contribution

It proposes the first definitions of computational solution concepts guaranteeing sequential rationality and introduces threat-free Nash equilibrium as a more flexible alternative to subgame perfection.

Findings

Revisits mediator implementation for correlated equilibria.

Proposes a variant protocol that is sequentially rational.

Provides insights into replacing mediators with stable protocols.

Abstract

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.