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, p_k(t) ∈ [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 p_k(t) using a criteria based on the comparison of their utilities with the

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... plest 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 p̅_eq and average equilibrium per-capita-income p̅_eq,U̅_∞. It turns out that the model exhibit some results that contradict the intuition. In particular, some games which - 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.