# Two-Stage Mechanism Design for Electric Vehicle Charging with Day-Ahead Reservations

## TL;DR

This paper introduces a two-stage mechanism for EV charging reservations, combining a posted-price real-time market with a VCG auction in the day-ahead market, balancing incentive compatibility, reservation awareness, and budget balance.

## Contribution

It proposes a novel two-stage mechanism integrating posted-price and VCG auction approaches to improve EV charging market efficiency and properties.

## Key findings

- The classical VCG mechanisms do not satisfy all desired properties.
- The proposed posted-price mechanism is reservation-aware and budget-balanced.
- Using a VCG auction in the day-ahead market enhances efficiency when valuations are correlated.

## Abstract

We propose a general two-period model where electrical vehicles (EVs) can reserve charging sessions in the day-ahead market and swap them in the real-time market. Under the model, we explore several candidate mechanisms for running the two markets, compared using several normative properties such as incentive compatibility, efficiency, reservation awareness, and budget balance. Specifically, reservation awareness is the only property coupling the two markets and dictates that an EV will not get a lower utility by joining the real-time market. Focusing on the real-time market, we show that two variants of the classical Vickrey-Clarke-Groves (VCG) mechanism do not satisfy all the proposed properties; specifically, one is not reservation-aware, while the other is not budget-balanced. Moreover, we show that no mechanism satisfies some combinations of the properties. Then, we propose to use a posted-price mechanism to resolve the issue, which turns out to be the dynamic pricing mechanism adopted in many real-world systems. The proposed mechanism has no efficiency guarantee but satisfies all the other properties. To improve efficiency, we propose to use a VCG auction in the day-ahead market that guides the reserve prices in the real-time market. When EVs' valuations in the two markets are highly correlated, the proposed approach results in highly efficient outcomes.