A network of agents cooperate on a given area. Time evolution of their power is described within a set of nonlinear equations. The limitation of resources is introduced via the Verhulst term, equivalent to a global coupling. Each agent is fed by some other agents from his neighborhood. Two subsequent stages of the time evolution can be observed. Initially, the richness of everybody increases distinctly, but its distribution becomes wide. After some transient time, however, resources are exhausted. Richness of some agents falls to zero and they are eliminated. Cooperation becomes less effective, what leads to subsequent falls. Finally, small percent of agents survive in a steady state. We investigate, how the cooperation influences the rate of surviving.