Fair Computation with Rational Players

We consider the problem of fairness in two-party computation, where this means (informally) that both parties should learn the correct output. A seminal result of Cleve (STOC 1986) shows that fairness is, in general, impossible to achieve for malicious parties. Here, we treat the parties as rational and seek to understand what can be done. Asharov et al. (Eurocrypt 2011) recently considered this problem and showed impossibility of rational fair computation for a particular function and a particular set of utilities. We observe, however, that in their setting the parties have no incentive to compute the function even in an ideal world where fairness is guaranteed. Revisiting the problem, we show that rational fair computation is possible, for arbitrary functions and utilities, as long as at least one of the parties has a strict incentive to compute the function in the ideal world. This gives a novel setting in which game-theoretic considerations can be used to circumvent an impossibility result in cryptography.