Nash Bargaining Solution for the Formation Control Problem

The formation control of a team of agents has been addressed by methodologies that bring together systems, graph, and game theories. In contrast to most methodologies based on noncooperative game theory, we propose a cooperative game theory approach for the problem centered on the Nash bargaining solution concept. The formation control problem for a team of agents with double integrator dynamics is formulated as a graphical game with an affine-quadratic structure. After characterizing the Nash equilibrium and the Pareto optimal solutions of the game, the Nash bargaining solution is obtained by a simple numerical procedure. An illustrative example shows the superiority of the Nash bargaining solution over the Nash equilibrium solution in terms of ease of implementation and performance of the team of agents.