cooperator (${\bf C}$), who in turn gets $s$, the sucker’s payoff. In case of mutual cooperation, each player obtains a reward $r$, while mutual defection punishes both players with the payoff $p$. The table is in fact very general, because the payoffs of the Prisoner’s Dilemma must satisfy the additional constraints $t>r>p>s$ and $2r>t+s$. Other relationships between the parameters define the Snowdrift and Stag Hunt games [@sza2].

In some versions of the game a different set of parameters is used: $r=c-b$, $s=-b$, $t=c$ and $p=0$ [@oht], to account for a slightly different interpretation of the game: a cooperator (C) is someone who pays a cost $c$ for any other individual to receive a benefit $b$. In turn, a defector does not distribute any benefits and gets those delivered by the cooperators at no cost.

To simplify the analysis, in the following we use a reduced version of the payoff table (Table 2), which has only one free parameter. It has been show that this parameter eduction preserves the most relevant features of the prisoner’s dilemma [@now0].

               [**C**]{}   [**D**]{}
  ----------- ----------- -----------
   [**C**]{}      $1$        $1-t$
   [**D**]{}      $t$         $0$

  : Reduced payoff table for the prisoner’s dilemma: the strategy in each row 