Effects of competition and cooperation interaction between agents on networks in the presence of a market capacity

A network effect is introduced taking into account competition, cooperation, and mixed-type interaction among agents along a generalized Verhulst-Lotka-Volterra model. It is also argued that the presence of a market capacity undoubtedly enforces a definite limit on the agent's size growth. The state stability of triadic agents, i.e., the most basic network plaquette, is investigated analytically for possible scenarios, through a fixed-point analysis. It is discovered that: (i) market demand is only satisfied for full competition when one agent monopolizes the market; (ii) growth of agent size is encouraged in full cooperation; (iii) collaboration among agents to compete against one single agent may result in the disappearance of this single agent out of the market; and (iv) cooperating with two rivals may become a growth strategy for an intelligent agent.