The Welfare Gap of Strategic Storage: Universal Bounds and Price Non-Linearity

2026-02-23

AI Summary

This study quantifies the efficiency loss in electricity markets arising from decentralized, self-interested energy storage operations relative to a centralized social welfare optimum. Within a continuous-time stochastic framework, the authors systematically compare the welfare gap between a central planner and individual operators by integrating continuous-time stochastic optimization, modeling of non-anticipative adaptive strategies, and convex analysis. Their key contributions include the first proof that under linear pricing, the welfare ratio admits a tight upper bound of 4/3 with structural invariance; the demonstration that efficiency losses can become unbounded under general convex pricing; and the establishment of a curvature-independent bound under monomial pricing—where the worst-case ratio does not exceed 2—highlighting that convexity of prices alone is insufficient to guarantee market efficiency.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

This paper studies the efficiency of battery storage operations in electricity markets by comparing the social welfare gain achieved by a central planner to that of a decentralized profit-maximizing operator. The problem is formulated in a generalized continuous-time stochastic setting, where the battery follows an adaptive, non-anticipating policy subject to periodicity and other constraints. We quantify the efficiency loss by bounding the ratio of the optimal welfare gain to the gain under profit maximization. First, for linear price functions, we prove that this ratio is tightly bounded by $4/3$. We show that this bound is a structural invariant: it is robust to arbitrary stochastic demand processes and accommodates general convex operational constraints. Second, we demonstrate that the efficiency loss can be unbounded for general convex price functions, implying that convexity alone is insufficient to guarantee market efficiency. Finally, to bridge these regimes, we analyze monomial price functions, where the degree controls the curvature. For specific discrete demand scenarios, we demonstrate that the ratio is bounded by $2$, independent of the degree.

Problem

• welfare gap
• strategic storage
• electricity markets
• market efficiency
• price non-linearity

Innovation

• strategic storage
• welfare gap
• price non-linearity
• efficiency bound
• stochastic electricity markets