Does the scale-free topology favor the emergence of cooperation?

In a recent Letter [F.C. Santos and J. M. Pacheco Phys. Rev. Lett. \textbf{95}, 098104 (2005)], the scale-free networks are found to be advantageous for the emergence of cooperation. In the present work an evolutionary prisoner's dilemma game with players located on Barab\'asi-Albert scale-free networks is studied in detail. The players are pure strategist and can follow two strategies: either to defect or to cooperate. Serval alternative update rules determining the evolution of each player's strategy are considered. Using systematic Monte Carlo simulations we have calculated the average density of cooperators as a function of the temptation to defect. It is shown that the results obtained by numerical experiments depend strongly on the dynamics of the game, which could lower the important of scale-free topology on the persistence of the cooperation. Particularly, the system exhibits a phase transition, from active state (coexistence of cooperators and defectors) to absorbing state (only defectors surviving) when allowing `` worse\rq\rq strategy to be imitated in the evolution of the game.