  Exploiting others is beneficial individually but it could also be detrimental
globally. The reverse is also true: a higher cooperation level may change the
environment in a way that is beneficial for all competitors. To explore the
possible consequence of this feedback we consider a coevolutionary model where
the local cooperation level determines the payoff values of the applied
prisoner's dilemma game. We observe that the coevolutionary rule provides a
significantly higher cooperation level comparing to the traditional setup
independently of the topology of the applied interaction graph. Interestingly,
this cooperation supporting mechanism offers lonely defectors a high surviving
chance for a long period hence the relaxation to the final cooperating state
happens logarithmically slow. As a consequence, the extension of the
traditional evolutionary game by considering interactions with the environment
provides a good opportunity for cooperators, but their reward may arrive with
some delay.
