  Quantum strategies are introduced into evolutionary games. The agents using
quantum strategies are regarded as invaders whose fraction generally is 1% of a
population in contrast to the 50% defectors. In this paper, the evolution of
strategies on networks is investigated in a defector-dominated population, when
three networks (Regular Lattice, Newman-Watts small world network, scale-free
network) are constructed and three games (Prisoners' Dilemma, Snowdrift,
Stag-Hunt) are employed. As far as these three games are concerned, the results
show that quantum strategies can always invade the population successfully.
Comparing the three networks, we find that the regular lattice is most easily
invaded by agents that adopt quantum strategies. However, for a scale-free
network it can be invaded by agents adopting quantum strategies only if a hub
is occupied by an agent with a quantum strategy or if the fraction of agents
with quantum strategies in the population is significant.
