An architectural view of game theoretic control

Abstract

Resource allocation has long been a fundamental research problem across several disciplines. While traditional approaches to this problem were centralized, recent research has focussed on distributed solutions for resource allocation, for reasons of scalability, reliability and efficiency in many realworld applications. Game-theoretic control is a promising new approach for distributed resource allocation. In this thesis, we describe how game-theoretic control can be viewed as having an intrinsic layered architecture, which provides a modularization that simplifies the control design.We illustrate this architectural view by presenting details about one particular instantiation using potential games as an interface. This example serves to highlight the strengths and limitations of the proposed architecture while also illustrating the relationship between game-theoretic control and other existing approaches to distributed resource allocation. We also demonstrate the power of this approach by reformulating the power control problem in sensor networks as a game-theoretic control problem in the potential games instantiation of our framework. This allows us to relax several assumptions made by previous contributions, and consider more complex objective functions. vi Contents Acknowledgements ivAbstract v

Distributed Welfare Games

“…Second, a system designer must specify a local behavioral or learning rule for each agent that specifies how an individual agent processes available information to formulate a decision. The overarching goal is to complete the two design steps, referred to as utility design and learning design, respectively, to ensure that the emergent global behavior is desirable (Arslan et al 2007, Marden et al 2009, Gopalakrishnan et al 2011). …”

State based potential games

“…Game theory is beginning to emerge as a valuable paradigm for the design and control of such multiagent systems Gopalakrishnan, Marden, & Wierman, 2011;Marden, Arslan, & Shamma, 2009a). Utilizing game theory for this purpose requires the following two step design process: (i) define the interaction framework of the agents within a game theoretic environment (game design) and (ii) define local decision making rules that specify how each agent processes available information to formulate a decision (learning design).…”

“…The goal is to complete both steps (i) and (ii) to ensure that the collective behavior converges to a desirable operating point, e.g., a pure Nash equilibrium of the designed game. One of the major appeals of using game theory for multiagent systems is that game theory provides a hierarchical decomposition between the design of the interaction framework and the design of the learning rules (Gopalakrishnan et al, 2011). For example, if the interaction framework is designed as a potential game (Monderer & Shapley, 1996) then any learning algorithm for potential games can be utilized as a distributed control algorithm with provable guarantees on the emergent collective behavior.…”

Potential Games Are Necessary to Ensure Pure Nash Equilibria in Cost Sharing Games

“…Other notable specializations of our model that focus on the design of distribution rules are network coding (Marden and Effros [26]), graph coloring (Panagopoulou and Spirakis [37]), and coverage problems (Marden and Wierman [28], Marden and Wierman [29]). Designing distribution rules in our cost sharing model also has applications in distributed control (Gopalakrishnan et al [16]). …”