A simple model for cooperation between "selfish" agents, which play an
extended version of the Prisoner's Dilemma(PD) game, in which they use
arbitrary payoffs, is presented and studied. A continuous variable,
representing the probability of cooperation, pkβ(t)β [0,1], is assigned to
each agent k at time t. At each time step t a pair of agents, chosen at
random, interact by playing the game. The players update their pkβ(t) using a
criteria based on the comparison of their utilities with the simplest estimate
for expected income. The agents have no memory and use strategies not based on
direct reciprocity nor 'tags'. Depending on the payoff matrix, the systems
self-organizes - after a transient - into stationary states characterized by
their average probability of cooperation pΛβeqβ and average equilibrium
per-capita-income pΛβeqβ,UΛββ. It turns out that the model
exhibit some results that contradict the intuition. In particular, some games
which - {\it a priory}- seems to favor defection most, may produce a relatively
high degree of cooperation. Conversely, other games, which one would bet that
lead to maximum cooperation, indeed are not the optimal for producing
cooperation.Comment: 11 pages, 3 figures, keybords: Complex adaptive systems, Agent-based
models, Social system