In the present paper, the case of a database of scientific articles is described. There can be observed the quantitative effects of the increasing strength of cooperation between scholars. It is manifested in time-related features changes of the numbers distribution of a single co-authors’ article. The distribution of the number of co-authors of an article recorded in the database evolves with time from a profile with no more than one author to a profile with several authors. A social dilemma model is proposed to explain the dynamics of changes in the distribution of the number of co-authors. The most successful strategy of the three considered alternative strategies of cooperation is selected.