This is the full version of a paper submitted to the Computability in Europe (CiE 2023) conference, with all proofs omitted there. In 2012 P. D. Azar and S. Micali introduced a new model of interactive proofs, called "Rational Interactive Proofs". In this model the prover is neither honest nor malicious, but rational in terms of maximizing his expected reward. In this article we explore the connection of this area with classic complexity results. In the first part of this article we revise the ties between the counting hierarchy and the hierarchy of constant-round rational proofs. We prove that a polynomial-time machine with oracle access to DRMA[k] decides exactly languages in DRMA[k], a coincidence unknown for levels of the counting hierarchy. In the second part we study communication complexity of single-round rational proofs. We show that the class defined by logarithmic-communication single-round rational proofs coincides with PP. We also show that single-round rational protocols that treat problems in Parity-P as black-box samplers of a random variable require at least a linear number of bits of communication.

翻译：本文是提交至欧洲可计算性会议（CiE 2023）论文的完整版本，其中省略了所有证明。2012年，P. D. Azar与S. Micali提出了一种称为"理性交互证明"的新型交互证明模型。在该模型中，证明者既非诚实也非恶意，而是以最大化期望收益为目标的理性主体。本文探讨了该领域与经典复杂性理论结果之间的关联。第一部分重新审视了计数层级与常轮理性证明层级之间的对应关系。我们证明：具有DRMA[k]预言机访问能力的多项式时间机器可精确判定DRMA[k]中的语言，这一结论在计数层级的各个层次中尚未知晓。第二部分研究了单轮理性证明的通信复杂度。我们证明：对数通信量的单轮理性证明所定义的类等价于PP类。同时表明，将Parity-P问题视为随机变量黑箱采样器的单轮理性协议至少需要线性比特的通信量。