Byzantine Agreement with a Rational Adversary

Traditionally, cryptographers assume a "worst-case" adversary who can act arbitrarily. More recently, they have begun to consider rational adversaries who can be expected to act in a utility-maximizing way. Here we apply this model for the first time to the problem of Byzantine agreement (BA) and the closely related problem of broadcast, for natural classes of utilities. Surprisingly, we show that many known results (e.g., equivalence of these problems, or the impossibility of tolerating t≥n/2 corruptions) do not hold in the rational model. We study the feasibility of information-theoretic (both perfect and statistical) BA assuming complete or partial knowledge of the adversary's preferences. We show that perfectly secure BA is possible for t<n corruptions given complete knowledge of the adversary's preferences, and characterize when statistical security is possible with only partial knowledge. Our protocols have the added advantage of being more efficient than BA protocols secure in the traditional adversarial model.