Games in Product Form for Demand Response Modelling
Thomas Buchholtzer, Michel de Lara
TL;DR
The paper addresses demand response in modern power systems by casting leader–follower interactions as W-games, a formal framework that explicitly models information structure, private knowledge, and beliefs under uncertainty. It introduces the W-model (Witsenhausen intrinsic model) to represent agents, Nature, actions, and information fields, and extends it to W-games where each player has a payoff/belief or risk measure, yielding a general Nash equilibrium and Stackelberg-type notions tailored to complex information structures. The authors reformulate several DR problems from the literature into the W-game form, highlighting often overlooked informational aspects, and provide a Thai DR program application to illustrate practical design and analysis. The work offers a modular, scalable approach to energy management problems with static or dynamic, single- or multi-actor configurations, enabling rigorous treatment of information asymmetry in bilevel and multi-level settings. Overall, the framework facilitates consistent modeling, analysis, and design of incentive mechanisms and pricing strategies in demand response, with potential for broad application in smart grids and aggregator-based markets.
Abstract
Energy systems are changing rapidly. More and more, energy production is becoming decentralized, highly variable and intermittent (solar, wind), while demand is diversifying (electric vehicles). As a result, balancing supply and demand is becoming more complex, making the adjustment of demand an interesting tool. Demand response is a typical leader-follower problem: a consumer (follower) adjusts his energy consumption based on the prices (or any other incentive) set by the supplier (leader). We propose a versatile and modular framework to address any leader-follower problem, focusing on the handling of often overlooked informational issues. First, we introduce a model that defines the rules of the game (W-model): agents are decision-makers, and Nature encapsulates everything beyond their control, such as private knowledge and exogenous factors. Following the so-called Witsenhausen intrinsic model, we present an efficient way to represent - on a product set, equipped with a product $σ$-algebra - the information available to agents when making decisions. Next, we introduce Games in Product Form (W-games) by equipping each player (a group of agents) with preferences (objective function and belief) over different outcomes. Thereby, we incorporate an additional layer of information, the characteristics of the preferences linked to players, which affects the possible definitions of an equilibrium. We make this explicit in Nash and Stackelberg equilibria. Equipped with this framework, we reformulate several papers on demand response, highlighting overlooked informational issues. We also provide an application based on the Thailand demand response program.