  In this paper we analyze from the game theory point of view Byzantine Fault
Tolerant blockchains when processes exhibit rational or Byzantine behavior. Our
work is the first to model the Byzantine-consensus based blockchains as a
committee coordination game. Our first contribution is to offer a
game-theoretical methodology to analyse equilibrium interactions between
Byzantine and rational committee members in Byzantine Fault Tolerant
blockchains. Byzantine processes seek to inflict maximum damage to the system,
while rational processes best-respond to maximise their expected net gains. Our
second contribution is to derive conditions under which consensus properties
are satisfied or not in equilibrium. When the majority threshold is lower than
the proportion of Byzantine processes, invalid blocks are accepted in
equilibrium. When the majority threshold is large, equilibrium can involve
coordination failures , in which no block is ever accepted. However, when the
cost of accepting invalid blocks is large, there exists an equilibrium in which
blocks are accepted iff they are valid.
