Effects of Competition and Cooperation Interaction between Agents on Networks in Presence of a "Market Capacity"

TL;DR

This paper models the complex interactions of competition and cooperation among agents within networks, considering market capacity constraints, and analyzes the stability of small network structures to understand different market scenarios.

Contribution

It introduces a generalized Verhulst-Lotka-Volterra model incorporating mixed interactions and market capacity, providing analytical insights into agent stability and market dynamics.

Findings

Full competition can satisfy market demand if one agent monopolizes

Cooperation encourages agent growth

Collaboration can lead to the disappearance of a rival agent

Abstract

A network effect is introduced taking into account competition, cooperation and mixed-type interaction amongst agents along a generalized Verhulst-Lotka-Volterra model. It is also argued that the presence of a market capacity enforces an indubious 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 amongst 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.