A simple scaling of the effectiveness of supporting mutual cooperation in donor-recipient games by various reciprocity mechanisms

In donor-recipient games (DRG), one of the sub-classes of Prisoner's Dilemma (PD), it is well-known that a game structure is described by two parameters benefit (b) and cost (c) of cooperation. By means of a series of numerical experiments, we proved that the effectiveness of supporting mutual cooperation in DRG by various reciprocity mechanisms can be expressed in a single game structural parameter, b/c. This also implies that the dilemma strength in various donor-recipient games with various reciprocity mechanisms can be evaluated only by b/c, which is consistent with the previous novel finding by Nowak. It was also discussed whether this kind of parameterization idea can be extended to general games in PD game class.