The goal of this workshop is to provide an introduction into basic game-theoretic concepts and tools, and to showcase some recent applications of game theory in control of emerging large scale and distributed networked systems.  The workshop comprises the following topics.

Foundations of Game-Theoretic Framework for Networks and Control (Basar).  With its rich set of conceptual, analytical and algorithmic tools, game theory has emerged as providing a versatile and effective framework for addressing a multitude of issues in networks and control, including resilience, reliability and security in networked (control) systems. This expository talk will introduce the key elements of this modeling paradigm, and discuss various game-theoretic solution concepts, mostly within the framework of nonzero-sum games. Among these are the solution concepts of saddle point (for zero-sum games) and Nash equilibrium as well as Stackelberg equilibrium (for nonzerosum games), for both static and dynamic games, as well as stochastic games. The talk will also cover efficiency (or inefficiency) of these solutions within a non-cooperative mode of decision-making, their sensitivity to imprecision in modeling, and ways of coping with the presence of strategic adversaries. Further, the role of incentive (or disincentive) mechanisms in mitigating or totally eliminating the adverse effects of inefficiency, sensitivity, and adversarial impact will be discussed. The presentation will conclude with some specific applications of the game-theoretic framework in networked control, sensor networks, and cyber-physical systems.

Mean Field Control Theory and its Applications (Malhame).  The fundamental intuitions that underline the development of so called Mean Field Games (also known as Mean Field Control Theory) will be presented, as well as some of its foundational results for continuous time systems. The results for both linear and nonlinear continuous time systems will be discussed. Mean Field Control emerges as the natural tool for dealing with the coordination and decentralized control of systems made up of large aggregates of similar weakly interacting elements such as found in the natural world from herds, to fish schools, to beehives, to human societies. Such configurations also occur in manmade constructs such as economic systems and the Internet. We present applications of the linear quadratic versions of the theory, first to a collective navigation problem such as fish schooling; secondly, to a class of control problems in the area of smart grids, whereby large collections of energy storage capable devices such as electric water heaters, are coordinated to mitigate the variability of renewable energy sources.

Games, Information, and Networked Control (Marden).  Game theory is a well-established discipline in the social sciences that is primarily used for modeling social behavior. Traditionally, the preferences of the individual agents are modeled as utility functions and the resulting behavior is assumed to be an equilibrium concept associated with these modeled utility functions, e.g., Nash equilibrium. This is in stark contrast to the role of game theory in engineering systems where the goal is to design both the agents utility functions and an adaptation rule such that the resulting global behavior is desirable. The transition of game theory from a modeling tool for social systems to a design tool for engineering systems promotes several new research directions that we will discuss in this talk. In particular, this talk will focus on the following questions: (i) How to design admissible agent utility functions such that the resulting game possesses desirable properties, e.g., the existence and efficiency of pure Nash equilibria? (ii) How to design adaptation rules that lead to desirable system-wide behavior? and (iii) How does the information available to the agents impact achievable performance guarantees in distributed engineering systems?

Games on Time-varying Networks (Nedich).  This talk will present some special games arising in networked systems with dynamically changing connectivity structure and with limited access to the whole system information. Some examples of such games that will be discussed include Transferable Utility (TU) games, aggregative games and monotone Nash games on graphs, where the players can use the local neighborhoods to learn/estimate network wide quantities that affect their payoff/ cost functions. We will discuss distributed strategies such as decentralized gradient-play strategies that can result in a Nash equilibrium in the presence of imperfect information such as gradient noise and other forms of uncertainties. Also, the complexity estimates for such strategies will be discussed in terms of their scaling properties with the time and with the number of players.