Nash-Based Strategies for the Control of Extended Complex Systems

An extended complex system is a large scale hierarchical system controlled by two or more teams of decision-makers. The teams may have different objective functions, and often can be in direct conflict with each other. Within each team, the decision-makers must cooperate for the collective benefit of the team, but outside the team each member must compete with the decision-makers in the other teams. Decision-making in the context of such an extended complex system can be modeled as a new framework within the theory of games, called multi-team games. A multi-team game is a decision-making structure consisting of several interacting teams of cooperating decision-makers that are simultaneously in conflict with the other teams. In this dissertation, a new strategy, called Noninferior Nash strategy, is proposed to define optimal cooperative decisions for members of non-cooperative teams in an extended complex system. This strategy represents an equilibrium for the teams characterized by the property that no team has an incentive to unilaterally deviate, while maintaining cooperation among its members, in order to improve its overall team performance. The Noninferior Nash strategy in both static and dynamic systems is developed and its properties are investigated. In order to deal with the issue of non-uniqueness of the solution, a team structure that allows for a leader to oversee the overall performance of the team is introduced. The Noninferior Nash strategy with a Leader is formulated so as to select the particular Noninferior Nash strategy that is best for the team. To illustrate these concepts on a realistic system, we consider a practical example of a military air operation modeled as an extended complex system. The Nash Noninferior Strategies are investigated as possible solution concepts for dynamic teaming, team tasking, and unit task assignments and reassignments in the process of optimally planning of shared responsibilities and roles in the hierarchical deployment of the units in the combat. Simulation examples are presented to illustrate the effectiveness of these strategies in preserving the friendly force while destroying the defending enemy units.