  A simulation scheme of quantum version of Cournot's Duopoly is proposed, in
which there is a new Nash equilibrium that may be also Pareto optimal without
any entanglement involved. The unique property of this simulation scheme is
decoherence-free against the symmetric photon loss. Furthermore, we analyze the
effects of the asymmetric information on this simulation scheme and investigate
the case of asymmetric game caused by asymmetric photon loss. A second-order
phase transition-like behavior of the average profits of the firm 1 and firm 2
in Nash equilibrium can be observed with the change of the degree of asymmetry
of the information or the degree of "virtual cooperation". It is also found
that asymmetric photon loss in this simulation scheme plays a similar role with
the asymmetric entangled states in the quantum game.
  PACS numbers: 02.50.Le, 03.67.-a
