  Classical game theory addresses decision problems in multi-agent environment
where one rational agent's decision affects other agents' payoffs. Game theory
has widespread application in economic, social and biological sciences. In
recent years quantum versions of classical games have been proposed and
studied. In this paper, we consider a quantum version of the classical
Barro-Gordon game which captures the problem of time inconsistency in monetary
economics. Such time inconsistency refers to the temptation of weak policy
maker to implement high inflation when the public expects low inflation. The
inconsistency arises when the public punishes the weak policy maker in the next
cycle. We first present a quantum version of the Barro-Gordon game. Next, we
show that in a particular case of the quantum game, time-consistent Nash
equilibrium could be achieved when public expects low inflation, thus resolving
the game.
