Efficiency of pair formation in a model society

In a recent paper a set of differential equations was proposed to describe a social process, where pairs of partners emerge in a community. The choice was performed on a basis of attractive resources and of random initial preferences. An efficiency of the process, defined as the probability of finding a partner, was found to depend on the community size. Here we demonstrate, that if the resources are not relevant, the efficiency is equal to unity; everybody finds a partner. With this new formulation, about 80 percent of community members enter to dyads; the remaining 20 percent form triads.