Receding-Horizon Games with Tullock-Based Profit Functions for Electric Ride-Hailing Markets

TL;DR

The paper addresses charging coordination for electric ride-hailing markets under time-varying demand and energy costs using a receding-horizon, two-player game with a Tullock-based profit function that accounts for customer abandonments. It proves the existence and uniqueness of a Nash equilibrium for the horizon-based game and proposes a semi-decentralized VI-based algorithm with Armijo/KKT-based stopping criteria to compute it, enabling both open-loop and receding-horizon (MPC-like) implementations. Numerical results show that longer planning horizons improve profits and reduce abandonment by better anticipating demand and price fluctuations, while open-loop planning lacks disturbance responsiveness. The work offers a principled, scalable framework for dynamic EV charging in competitive ride-hailing markets and lays groundwork for extensions to more players and integrated electricity-market models.

Abstract

This paper proposes a receding-horizon, game-theoretic charging planning mechanism for electric ride-hailing markets. As the demand for ride-hailing services continues to surge and governments advocate for stricter environmental regulations, integrating electric vehicles into these markets becomes inevitable. The proposed framework addresses the challenges posed by dynamic demand patterns, fluctuating energy costs, and competitive dynamics inherent in such markets. Leveraging the concept of receding-horizon games, we propose a method to optimize proactive dispatching of vehicles for recharging over a predefined time horizon. We integrate a modified Tullock contest that accounts for customer abandonment due to long waiting times to model the expected market share, and by factoring in the demand-based electricity charging, we construct a game capturing interactions between two companies over the time horizon. For this game, we first establish the existence and uniqueness of the Nash equilibrium and then present a semi-decentralized, iterative method to compute it. Finally, the method is evaluated in an open-loop and a closed-loop manner in a simulated numerical case study.

Figures (7)

• Figure 1: The charging planning problem involves two companies solving a scheduling problem at each time step $k$, considering the current battery state of their fleet, forecasted ride-hailing demand, and charging prices over a time horizon $T$. They can either implement the schedule in an open-loop manner or create a closed-loop system by only executing the first element of the control trajectory and repeating the process.
• Figure 2: Time profiles of $\beta[k]$, $q[k]$ and $\varepsilon[k]$, determining the expected ride-hailing revenue, charging costs and customer abandonments.
• Figure 3: Open loop: Evolution of the company $a$'s state and applied control input during time frame $T_{\text{total}}$.
• Figure 4: Open loop: Evolution of the company $b$'s state and applied control input during time frame $T_{\text{total}}$.
• Figure 5: Open loop: Attained profits for $T=9$.

Theorems & Definitions (9)

• Definition 1: Nash equilibrium
• Theorem 1
• proof
• Lemma 1
• proof
• Theorem 2
• proof
• Lemma 2: Optimality test
• proof