Super-efficient rational proofs

Abstract

Information asymmetry is a central problem in both computer science and economics. In many fundamental problems, an uninformed principal wants to obtain some knowledge from an untrusted expert. This models several real-world situations, such as a manager's relation with her employees, or the delegation of computational tasks to workers over the internet. Because the expert is untrusted, the principal needs some guarantee that the provided knowledge is correct. In computer science, this guarantee is usually provided via a proof, which the principal can verify. Thus, a dishonest expert will always get caught and penalized. In many economic settings, the guarantee that the knowledge is correct is usually provided via incentives. That is, a game is played between expert and principal such that the expert maximizes her utility by being honest. A rational proof is an interactive proof where the prover, Merlin, is neither honest nor malicious, but rational. That is, Merlin acts in order to maximize his own utility. I previously introduced and studied Rational Proofs when the verifier, Arthur, is a probabilistic polynomial-time machine [3]. In this thesis, I characterize super-efficient rational proofs, that is, rational proofs where Arthur runs in logarithmic time. These new rational proofs are very practical. Not only are they much faster than their classical analogues, but they also provide very tangible incentives for the expert to be honest. Arthur only needs a polynomial-size budget, yet he can penalize Merlin by a large quantity if he deviates from the truth.