Rational Proofs with Multiple Provers

Abstract

Interactive proofs (IP) model a world where a verifier delegates computation to an untrustworthy prover, verifying the prover's claims before accepting them. IP protocols have applications in areas such as verifiable computation outsourcing, computation delegation, cloud computing, etc. In these applications, the verifier may pay the prover based on the quality of his work. Rational interactive proofs (RIP), introduced by Azar and Micali (2012), are an interactive-proof system with payments, in which the prover is rational rather than untrustworthy-he may lie, but only to increase his payment. Rational proofs leverage the prover's rationality to obtain simple and efficient protocols. Azar and Micali show that RIP=IP(=PSPACE), i.e., the set of provable languages stay the same with a single rational prover (compared to classic IP). They leave the question of whether multiple provers are more powerful than a single prover for rational and classical proofs as an open problem.In this paper we introduce multi-prover rational interactive proofs (MRIP). Here, a verifier cross-checks the provers' answers with each other and pays them according to the messages exchanged. The provers are cooperative and maximize their total expected payment if and only if the verifier learns the correct answer to the problem. We further refine the model of MRIP to incorporate utility gaps, which is the loss in payment suffered by provers who mislead the verifier to the wrong answer.We define the class of MRIP protocols with constant, noticeable and negligible utility gaps-the payment loss due to a wrong answer is O(1), 1/n O(1) and 1/2 n O(1) respectively, where n is the length of the input. We give tight characterization for all three MRIP classes. On the way, we resolve Azar and Micali's open problem-under standard complexity-theoretic assumptions, MRIP is not only more powerful than RIP, but also more powerful than MIP (classic multi-prover IP); and this is true even the utility gap is required to be constant. We further show that the full power of each MRIP class can be achieved using only two provers and three rounds of communication.

Cooperate Delegation of Computation for Rational Party Using Zero-Determinant Strategy Approach

“…In 2015, Hao and Rong [13] applied them to public goods game and repeated noise game. In 2016, Chen [14] studied rational proof problem which include multiple provers from the perspective of complexity. In model, a verifier can cross-check the answers received by asking several provers.…”

“…However, it is a consensus that current delegate computing always introduce expensive verification costs into the system. Recently, In [14], an extension of the Zerodeterminant Strategy from two-player games to multi-player games was studied. While in [18], Rong et al investigated the influence of the strategy-selection timescale, and found that cooperation can be promoted if one permits an individual with a high payoff to hold onto his/her successful strategy for longer,which was also originally mentioned in [6].…”

Rational Proofs against Rational Verifiers

“…Later, Guo et al [8] presented a one-round rational argument with polylogarithmic verification for all languages in P. Campanelli and Gennaro [4] studied the composability of rational proofs and presented a sequentially composable rational proof for arithmetic circuits. Chen, McCauley, and Singh [5] studied rational proofs that allows multiple provers, and showed that multiple rational provers are strictly more powerful than one.…”

Towards Attack and Defense Views of Rational Delegation of Computation

“…In 2014, Guo et al [20] studied rational arguments with limited computing capacity of provers. In 2016, Chen et al [21] studied the rational proof of multiple provers from complexity theory. In 2017, Inasawa and Yasunaga [22] proposed a three-message delegation scheme in which the verifier was rational.…”