Symmetric and Synchronous Communication in Peer-to-Peer Networks

Motivated by distributed implementation of game-theoretical algorithms, we study symmetric systems, i.e. systems of processes which are intuitively "treated on an equal footing", and the problem of attaining common knowledge between processes. We formalize our setting by defining symmetry notions and peer-to-peer networks in the context of Communicating Sequential Processes (CSP), due to the common knowledge creating effects of its synchronous communication primitives. We prove that full CSP makes common knowledge in symmetric peer-to-peer systems possible, but not the restricted version which disallows output statements in guards, implemented in the programming language occam.