Replicator dynamics of evolutionary games with different delays on costs and benefits

•Evolutionary games with different time delays on costs and benefits are examined.•Differing cost and benefit delays lead to Hopf bifurcations in the replicator dynamics.•Increasing the time delay can destabilize the mixed-strategy equilibrium.•Further increasing time delays can bring the mixed-strategy equilibrium back to stability.•Examples are shown for a Snowdrift game and a Division of Labor game.