Evolution of complex multicellular life began from the emergence of a life cycle involving the formation of cell clusters. The opportunity for cells to interact within clusters provided them with an advantage over unicellular life forms. However, what kind of interactions may lead to the evolution of multicellular life cycles? Here, we combine evolutionary game theory with a model for the emergence of multicellular groups to investigate how cell interactions can influence reproduction modes during the early stages of the evolution of multicellularity. In our model, the presence of both cell types is maintained by stochastic phenotype switching during cell division. We identify evolutionary optimal life cycles as those which maximize the population growth rate. Among all interactions captured by two-player games, the vast majority promotes two classes of life cycles: (i) splitting into unicellular propagules or (ii) fragmentation into two offspring clusters of equal (or almost equal) size. Our findings indicate that the three most important characteristics, determining whether multicellular life cycles will evolve, are the average performance of homogeneous groups, heterogeneous groups, and solitary cells.