  The self-organization in cooperative regimes in a simple mean-field version
of a model based on "selfish" agents which play the Prisoner's Dilemma (PD)
game is studied. The agents have no memory and use strategies not based on
direct reciprocity nor 'tags'. Two variables are assigned to each agent $i$ at
time $t$, measuring its capital $C(i;t)$ and its probability of cooperation
$p(i;t)$. At each time step $t$ a pair of agents interact by playing the PD
game. These 2 agents update their probability of cooperation $p(i)$ as follows:
they compare the profits they made in this interaction $\delta C(i;t)$ with an
estimator $\epsilon(i;t)$ and, if $\delta C(i;t) \ge \epsilon(i;t)$, agent $i$
increases its $p(i;t)$ while if $\delta C(i;t) < \epsilon(i;t)$ the agent
decreases $p(i;t)$. The 4!=24 different cases produced by permuting the four
Prisoner's Dilemma canonical payoffs 3, 0, 1, and 5 -
corresponding,respectively, to $R$ (reward), $S$ (sucker's payoff), $T$
(temptation to defect) and $P$ (punishment) - are analyzed. It turns out that
for all these 24 possibilities, after a transient,the system self-organizes
into a stationary state with average equilibrium probability of cooperation
$\bar{p}_\infty$ = constant $ > 0$.Depending on the payoff matrix, there are
different equilibrium states characterized by their average probability of
cooperation and average equilibrium per-capita-income
($\bar{p}_\infty,\bar{\delta C}_\infty$).
