Variable investment, the Continuous Prisoner's Dilemma, and the origin of cooperation

Cooperation is fundamental to many biological systems. A common metaphor fo r studying the evolution of cooperation is the Prisoner's Dilemma, a game w ith two strategies: cooperate or defect. However, cooperation is rarely all or nothing, and its evolution probably involves the gradual extension of i nitially modest degrees of assistance. The inability of the Prisoner's Dile mma to capture this basic aspect limits its use for understanding the evolu tionary origins of cooperation. Here we consider a framework for cooperatio n based on the concept of investment: an act which is costly, but which ben efits other individuals, where the cost and benefit depend on the level of investment made. In the resulting Continuous Prisoner's Dilemma the essenti al problem of cooperation remains: in the absence of any additional structu re non-zero levels of investment cannot evolve. However, if investments are considered in a spatially structured context, selfish individuals who make arbitrarily low investments can be invaded by higher-investing mutants. Th is results in the mean level of investment evolving to significant levels, where it is maintained indefinitely. This approach provides a natural solut ion to the fundamental problem of how cooperation gradually increases from a non-cooperative state.