The designs of many new blockchains are inspired by the Byzantine fault tolerance (BFT) problem. While traditional BFT protocols assume most system nodes behave honestly, we recognize that blockchains are deployed in environments where nodes are subject to strategic incentives. This paper thus develops an economic framework for analyzing distributed consensus formation with explicit incentive considerations. We formalize the consensus formation process in a dynamic game with imperfect information and preplay communication where non-Byzantine nodes are Knightian uncertain about Byzantine actions, and characterize all of its symmetric equilibria. Our findings enrich those from traditional BFT algorithms, offer guidance for designing blockchains in trustless environments, and also provide a theoretical framework bridging distributed consensus and game theoretical modeling.
