The analysis of patterns of social interaction plays an important role in providing services on online platforms (e.g., in designing algorithms for the allocation of information resources). The proposed model takes into account human factors underlying the concept of the Ideal Free Distribution (IFD), which captures empirical patterns of the aggregate group-level behavior of individuals competing for resources. The model explains the phenomenon of resource undermatching as a natural IFD-based outcome resulting from boundedly rational decision-making (i.e., individuals perceive only some of the available resources). We show that undermatching can be described as a globally balanced state in which the perceived cost of the best forgone alternatives is approximately the same for all individuals. Furthermore, we identify conditions that guarantee stability. From this analysis, we infer that the matching of the aggregate of individual choices to resources is independent of their initial distribution. Finally, we quantify the effect of resource scarcity on the degree of matching.