In this paper we analyze from the game theory point of view Byzantine Fault Tolerantblockchains when processes exhibit rational or Byzantine behavior. Our work is the first tomodel the Byzantine-consensus based blockchains as a committeecoordination game. Ourfirstcontribution is to offer a game-theoretical methodology to analyseequilibrium interactions be-tween Byzantine and rational committee members in Byzantine FaultTolerant blockchains.Byzantine processes seek to inflict maximum damage to the system,while rational processesbest-respond to maximise their expected net gains. Oursecondcontribution is to derive condi-tions under which consensus properties are satisfied or not in equilibrium. When the majoritythreshold is lower than the proportion of Byzantine processes, invalid blocks are accepted inequilibrium. When the majority threshold is large, equilibrium can involvecoordination fail-ures, in which no block is ever accepted. However, when the cost ofaccepting invalid blocks islarge, there exists an equilibrium in which blocks are accepted iff they are valid.