  The last two decades have witnessed a rapid development of quantum
information processing, a new paradigm which studies the power and limit of
"quantum advantages" in various information processing tasks. Problems such as
when quantum advantage exists, and if existing, how much it could be, are at a
central position of these studies. In a broad class of scenarios, there are,
implicitly or explicitly, at least two parties involved, who share a state, and
the correlation in this shared state is the key factor to the efficiency under
concern. In these scenarios, the shared \emph{entanglement} or \emph{discord}
is usually what accounts for quantum advantage. In this paper, we examine a
fundamental problem of this nature from the perspective of game theory, a
branch of applied mathematics studying selfish behaviors of two or more
players. We exhibit a natural zero-sum game, in which the chance for any player
to win the game depends only on the ending correlation. We show that in a
certain classical equilibrium, a situation in which no player can further
increase her payoff by any local classical operation, whoever first uses a
quantum computer has a big advantage over its classical opponent. The
equilibrium is fair to both players and, as a shared correlation, it does not
contain any discord, yet a quantum advantage still exists. This indicates that
at least in game theory, the previous notion of discord as a measure of
non-classical correlation needs to be reexamined, when there are two players
with different objectives.
