Stability robustness conditions for market power analysis in industrial organization networks

Business networks provide one of the most compelling environments to study the conflicting effects of competition and cooperation on multi-agent dynamical systems. While firms engage various merger and divestiture strategies to create the desired cooperative environment that enhances their market power, governmental regulatory agencies enforce antitrust measures that protect competition as a means to limit the market power of these organizations. Merger simulation has subsequently evolved in recent years as a mechanism to study the impact of different organizational structures on the market. Nevertheless, typical economic models can often lead to competition dynamics that arbitrarily lose stability when considering different organizational structures. This work provides stability robustness conditions with respect to coalition structure for profit-maximizing dynamical systems with network demand, and partially convex utility. In particular, we show that stability of the coalition of all agents is sufficient to guarantee stability of all other coalition structures. These conditions are then leveraged to provide a systematic methodology for estimating a rich variety of demand systems that guarantee sensible stability results regardless of the structure of cooperation in the marketplace.