Rational Proofs with Non-Cooperative Provers

Interactive-proof-based approaches are widely used in verifiable computation outsourcing. The verifier models a computationally-constrained client and the provers model powerful service providers. In classical interactive-proof models with multiple provers, the provers' interests either perfectly align (e.g. MIP) or directly conflict (e.g. refereed games). However, service providers participating in outsourcing applications may not meet such extremes. Instead, each provider may be paid for his service, while he acts solely in his own best interest. An active research area in this context is rational interactive proofs (RIP), in which the provers try to maximize their payment. However, existing works consider either a single prover, or multiple provers who cooperate to maximize their total payment. None of them truly capture the strategic nature of multiple service providers. How to define and design non-cooperative rational interactive proofs is a well-known open problem. We introduce a multi-prover interactive-proof model in which the provers are rational and non-cooperative. That is, each prover acts individually so as to maximize his own payment in the resulting game. This model generalizes single-prover rational interactive proofs as well as cooperative multi-prover rational proofs. This new model better reflects the strategic nature of service providers from a game-theoretic viewpoint. To design and analyze non-cooperative rational interactive proofs (ncRIP), we define a new solution concept for extensive-form games with imperfect information, strong sequential equilibrium. Our technical results focus on protocols which give strong guarantees on utility gap, which is analogous to soundness gap in classical interactive proofs. We give tight characterizations of the class of ncRIP protocols with constant, noticeable, and negligible gap.