  Nash equilibrium is employed to find a game theoretic robust security bound
on quantum bit error rate (QBER) for DL04 protocol which is a scheme for
quantum secure direct communication that has been experimentally realized
recently. The receiver, sender and eavesdropper (Eve) are considered to be
quantum players (players having the capability to perform quantum operations).
Specifically, Eve is considered to have the capability of performing quantum
attacks (e.g., W\'ojcik's original attack, W\'ojcik's symmetrized attack and
Pavi\v{c}i\'c attack) and classical intercept and resend attack. Game theoretic
analysis of the security of DL04 protocol in the above scenario is performed by
considering several game scenarios. The analysis revealed the absence of a
Pareto optimal Nash equilibrium point within these game scenarios.
Consequently, mixed strategy Nash equilibrium points are identified and
employed to establish both upper and lower bounds for QBER. Further, the
vulnerability of the DL04 protocol to Pavi\v{c}i\'c attack in the message mode
is established. In addition, it is observed that the quantum attacks performed
by Eve are more powerful than the classical attack, as the QBER value and the
probability of detecting Eve's presence are found to be lower in quantum
attacks compared to classical ones.
