An evolutionary edge of knowing less (or: On the 'curse' of global information)

Consider a population of farmers who live around a lake. Each farmer engages in trade with his two adjacent neighbors. The trade is governed by a prisoner's dilemma 'rule of engagement.' A farmer's payoff is the sum of the payoffs from the two prisoner's dilemma games played with his two neighbors. When a farmer dies, his son takes over. The son decides whether to cooperate or defect by considering the actions taken and the payoffs received by the most prosperous members of the group comprising his own father and a set of his father's neighbors. The size of this set, which can vary, is termed the 'span of information.' It is shown that a larger span of information can be detrimental to the stable coexistence of cooperation and defection, and that in well-defined circumstances, a large span of information leads to an end of cooperation, whereas a small span does not. Conditions are outlined under which, when individuals' optimization is based on the assessment of less information, the social outcome is better than when optimization is based on an assessment of, and a corresponding response to, more information.