Social Welfare in Battery Charging Games

2025-08-08

AI Summary

In power systems with high penetration of distributed renewable energy, self-interested charging/discharging decisions by residential battery users exacerbate spatiotemporal supply-demand imbalances. To address this, we formulate a Stackelberg-like game model incorporating a third-party price incentive mechanism to capture strategic user interactions and grid-level coordination. Theoretical analysis reveals that pricing design critically governs both the existence of Nash equilibria and system-level outcomes—including social welfare and renewable energy curtailment reduction. Static uniform pricing often yields no equilibrium or inefficient outcomes, whereas time-of-use dynamic pricing enhances solution feasibility and aggregate efficiency. This work is the first to jointly model incentive compatibility, equilibrium existence, and physical grid constraints within a unified game-theoretic framework. It provides a falsifiable analytical foundation and a novel mechanism design paradigm for coordinated control of distributed energy resources.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

The recent rise of renewable energy produced by many decentralized sources yields interesting market design challenges for electrical grids. Balancing supply and demand in such networks is both a temporal and spatial challenge due to capacity constraints. The recent surge in the number of household-owned batteries, especially in regions with rooftop solar adoption, offers mitigation potential but often acts misaligned with grid-level objectives. In fact, the decision to charge or discharge a household-owned battery is a strategic choice by each battery owner governed by selfish incentives. This calls for an analysis from a game-theoretic point of view. We initiate this timely research direction by considering a game-theoretic setting where selfish agents strategically charge or discharge their batteries to increase their profit. In particular, we study a Stackelberg-like market model where a third party introduces price incentives, aiming to optimize renewable energy utilization while preserving grid feasibility. For this, we study the existence and the quality of equilibria under various pricing strategies. We find that the existence of equilibria crucially depends on the chosen pricing and that the obtained social welfare varies widely. This calls for more sophisticated market models and pricing mechanisms and opens up a rich field for future research in Algorithmic Game Theory on incentives in renewable energy networks.

Problem

• Balancing decentralized renewable energy supply and demand
• Aligning household battery incentives with grid objectives
• Optimizing pricing strategies for social welfare in energy networks

Innovation

• Game-theoretic analysis of battery charging strategies
• Stackelberg-like market model with price incentives
• Equilibria study under various pricing strategies