  This paper presents a novel solution concept, called BAR Nash Equilibrium
(BARNE) and apply it to analyse the Verifier's dilemma, a fundamental problem
in blockchain. Our solution concept adapts the Nash equilibrium (NE) to
accommodate interactions among Byzantine, altruistic and rational agents, which
became known as the BAR setting in the literature. We prove the existence of
BARNE in a large class of games and introduce two natural refinements, global
and local stability. Using this equilibrium and its refinement, we analyse the
free-rider problem in the context of byzantine consensus. We demonstrate that
by incorporating fines and forced errors into a standard quorum-based
blockchain protocol, we can effectively reestablish honest behavior as a
globally stable BARNE.
