Utility Design for Distributed Resource Allocation -- Part I: Characterizing and Optimizing the Exact Price of Anarchy

Game theory has emerged as a fruitful paradigm for the design of networked multiagent systems. A fundamental component of this approach is the design of agents' utility functions so that their self-interested maximization results in a desirable collective behavior. In this work we focus on a well-studied class of distributed resource allocation problems where each agent is requested to select a subset of resources with the goal of optimizing a given system-level objective. Our core contribution is the development of a novel framework to tightly characterize the worst case performance of any resulting Nash equilibrium (price of anarchy) as a function of the chosen agents' utility functions. Leveraging this result, we identify how to design such utilities so as to optimize the price of anarchy through a tractable linear program. This provides us with a priori performance certificates applicable to any existing learning algorithm capable of driving the system to an equilibrium. Part II of this work specializes these results to submodular and supermodular objectives, discusses the complexity of computing Nash equilibria, and provides multiple illustrations of the theoretical findings.Comment: 15 pages, 5 figure

Building cluster control to enable grid reliability and efficiency support

Power system operators are actively seeking solutions to increase electric grid power flexibility and inertia, to accommodate deeper renewable integration. Buildings account for 75% of the total electricity use in the US and have great potential for grid reliability support at various time and spatial scales. Due to the limited bidding power of individual buildings, grid services are often provided by a fleet of small buildings managed by tailored coordination strategies. This dissertation presents two families of control methods for building cluster energy management based on the control time frequency and inter-building coordination mode: (1) dictatorial load modulating control strategies formulated under a specific context of distribution voltage regulation, and (2) market-based load shifting control achieved through a game-theoretic control framework. Load modulating represents the ability to balance power supply and demand within seconds in response to the grid signal. Therefore, the load modulating can enable distribution voltage support by controlling flexible loads in the building clusters to let their power use follow volatile solar photovoltaic output, as a means to mitigate fluctuations in the net demand and maintain a stable voltage. Load shifting represents the ability to change the timing of electricity use. In load shifting the typical time duration is 1 to 4 hours, and response time is less than 1 hour. The game-theoretic control strategies allow coordinative load shifting in which individual entities determine their control actions in their own interests while coordination is achieved indirectly through a market mechanism, with the goal of flattening the total load curve of the building cluster