Resource Allocation in Electricity Markets with Budget Constrained Customers

2026-03-17

AI Summary

This study addresses the challenge of welfare maximization under budget constraints in electricity markets, where users’ optimization problems are typically non-convex and difficult to solve. The authors propose an explicit piecewise-modified utility function constructed by splicing the original utility with a logarithmic function, thereby transforming the problem into a convex optimization formulation under tight budget constraints. Leveraging this reformulation, they establish the existence and uniqueness of a competitive equilibrium and demonstrate its equivalence to the solution of the modified convex welfare maximization problem. A dual ascent algorithm is employed to compute the equilibrium, and its convergence—along with the validity of the resulting equilibrium—is corroborated through theoretical analysis and numerical experiments using quadratic and square-root utility functions.

Technology Category

• Search and Optimization: Non-convex Optimization
• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements

Abstract

In electricity markets, customers are increasingly constrained by their budgets. A budget constraint for a user is an upper bound on the price multiplied by the quantity. However, since prices are determined by the market equilibrium, the budget constrained welfare maximization problem is difficult to define rigorously and to work with. In this letter, we show that a natural dual-ascent algorithm converges to a unique competitive equilibrium under budget constraints. Further, this budget-constrained equilibrium is exactly the solution of a convex welfare maximization problem in which each user's utility is replaced by a modified utility that splices the original utility with a logarithmic function where the budget binds. We also provide an explicit piecewise construction of this modified utility and demonstrate the results on examples with quadratic and square root utility functions.

Problem

• electricity markets
• budget constraints
• welfare maximization
• market equilibrium
• resource allocation

Innovation

• budget constraints
• competitive equilibrium
• convex welfare maximization
• dual-ascent algorithm
• modified utility function