Development of cooperative relationships through increasing investment.

Reciprocal altruism can become established among selfish, unrelated individuals if they use responsive strategies such as 'tit-for-tat. This result raises the fundamental question: how altruistic should one be? The problem is difficult to solve using current 'prisoner's dilemma' based models because they allow only the discrete choice of cooperating or defecting. In reality, however, cooperation is rarely all-or-nothing. Furthermore, if cooperative investment is variable, a new and more subtle kind of cheating becomes possible: individuals may invest slightly less than their partner. A concern is that this 'short-changing' will erode cooperative ventures. Here we show that cooperation can thrive despite variable investment through the new strategy of 'raise-the-stakes'. This strategy offers a small amount on first meeting and then, if matched, raises its investment, something that no strategy in the discrete model can do. We show that such behaviour can readily invade a population of non-altruists and cannot be effectively exploited. The practice of 'testing the water' rather than making sudden cooperative 'leaps of faith' powerfully reinforces the stability and effectiveness of reciprocity.