Altruistic agents in uncertain dynamic games

The distributed operation of dynamic systems, such as traffic networks and the power grid, can be viewed as a dynamic game among their control agents. As the agents respond to one another’s decisions by resolving their problems, they trace a trajectory in decision space that, if convergent, arrives at a fixed point. Thus, two issues of concern are the convergence to attractors and their location relative to Pareto optimal solutions. This paper addresses these issues in games where each agent continually solves a problem from a family of unconstrained, but general optimization problems. Specifically, it delivers simple yet effective problem transformations to influence the convergence to and location of attractors—these transformations are referred to as altruistic factors and the agents that implement them are called altruistic agents. This paper proposes algorithms to draw attractors towards Pareto optimal solutions: for the case of quadratic functions, a thorough analysis of the rate of convergence is provided; for the case of general functions, a trust-region-based algorithm is proposed. An application of this game-theoretic framework is improvement of the quality of the solutions attained by distributed model predictive control, particularly in scenarios whose objective functions are quadratic and whose dynamics are linear.