Regulating EV Charging Markets for Fairness: Incentives for Pricing and Capacity Decisions

Abstract: The transition to electric mobility calls for charging infrastructure that is both efficient and socially equitable. This paper examines fairness in electric vehicle (EV) charging station pricing and capacity through a game-theoretic perspective. We model a non-cooperative market in which competing charging service providers set prices and capacities while customers choose stations based on generalized cost, leading to a market equilibrium. We then benchmark this decentralized outcome against an idealized planner solution that jointly optimizes efficiency and equity. To align market outcomes with socially desirable goals, we design targeted incentives that guide operators toward more fair charger placement. Case studies demonstrate that unregulated competition tends to exacerbate disparities in charger access across demographic groups, whereas carefully calibrated incentives can reduce inequities without significant efficiency loss. The framework provides insights for policymakers on reconciling free-market dynamics with the broader societal goals of fairness in electrified mobility systems.

• The paper develops a bi-level game-theoretic model combining charge point operator pricing and capacity competition with stochastic user equilibrium, then compares decentralized outcomes with utilitarian and Nash Bargaining fairness benchmarks.
• The study finds that decentralized operators strategically underinvest in capacity, while the utilitarian allocation achieves 799.9 minutes of total travel time and the fairness-oriented allocation requires 1,028.3 minutes—about 29% more.
• The paper proposes an iterative per-unit capacity subsidy that redirects investment toward underserved stations, reduces travel-time disparities, and moves market outcomes toward fairness, although its efficiency impact and scalability remain unvalidated.

Overview

This paper develops a game-theoretic framework for evaluating and correcting inequities in electric vehicle (EV) charging markets. The authors—Wang, Hu, Yu, and Moura, affiliated with UC Berkeley, KTH Royal Institute of Technology, and Nanyang Technological University—model a non-cooperative oligopoly of Charge Point Operators (CPOs) that simultaneously set prices and charging capacities while customers allocate demand across stations via stochastic user equilibrium. The central contribution is a three-part construction: (i) a bi-level model capturing the decentralized market equilibrium, (ii) centralized planner benchmarks that incorporate both utilitarian efficiency and distributional fairness via the Nash Bargaining Solution (NBS), and (iii) an iterative per-unit capacity subsidy mechanism designed to steer the decentralized equilibrium toward the fairness-oriented allocation. The work is motivated by the observation that prior equity-oriented studies of charger placement do not model the profit-driven market structure in which CPO decisions are actually made.

Decentralized market equilibrium

The lower level models $N$ customers choosing among $M$ stations through a Multinomial Logit (MNL) discrete choice model. Each customer minimizes a generalized cost combining the monetary price $p_j$ and time cost $\tau \cdot T_j$, where travel/charging time follows a linear congestion function with free-flow detour component $T_{j,0}$ and a congestion term increasing in demand $q_j$ and decreasing in capacity $c_j$. Because costs depend endogenously on flows, the customer problem is a fixed-point system resolved to a stochastic user equilibrium via the Method of Successive Averages (MSA).

The upper level treats each station as a rational profit-maximizing agent selecting $(p_j, c_j)$ subject to non-negativity constraints. Profit is revenue minus energy purchase costs, a monetary penalty for congestion experienced by its customers, and capital investment costs $K_j$ per unit capacity. The resulting structure is a nested equilibrium: user-level SUE embedded within operator-level Nash equilibrium over pricing and capacity. Notably, the profit function internalizes the congestion penalty borne by a station's own customers, which shapes operators' incentive to deliberately avoid oversizing capacity—a behavior the results section confirms empirically.

The solution algorithm combines MSA for flows, L-BFGS-B quasi-Newton optimization for each station's continuous best-response (with capacities rounded to integers afterward), and a diagonalization scheme iterating best responses until no station can improve profit by unilateral deviation. The centralized problems are solved with Gurobi 12.0.3.

Centralized benchmarks: utilitarian and fairness-based planning

Two planner scenarios serve as reference points, both constrained to the same total capacity as the decentralized outcome for comparability. The utilitarian benchmark minimizes aggregate opportunity cost $\sum_j o_j = \sum_j q_j \tau T_j$. The fairness benchmark adopts an NBS-inspired objective maximizing the product of group-level improvements over a benchmark allocation $M$0, implemented as minimizing $M$1. The authors position this criterion between pure utilitarianism (which may sacrifice disadvantaged groups) and Rawlsian max-min fairness (which prioritizes only the worst-off group). The domain constraint $M$2 for all groups is required; the benchmark $M$3 is taken from the initial decentralized equilibrium utilities.

An important structural caveat: the fairness formulation captures only one dimension of equity—equalizing total time costs across stations—and reduces the influence of initial travel distance on outcomes. It does not address demographic or socioeconomic heterogeneity, a limitation the authors acknowledge explicitly.

Results: decentralization versus planning

In the experimental setting ($M$4 customers, $M$5 stations, logit sensitivity $M$6, value of time $M$7, congestion parameter $M$8, capital cost $M$9 USD/charger, operating cost $p_j$0 USD/customer), three findings emerge:

• Strategic under-capacity: In the decentralized equilibrium, popular stations deliberately maintain congestion to sustain high prices, exploiting captive demand near the main road.
• Utilitarian concentration: The utilitarian planner concentrates chargers at the most accessible station (lowest $p_j$1), achieving the lowest total travel time of 799.9 minutes. However, the authors argue this is a local optimum vulnerable to real-world land constraints and corridor-level network effects, and it produces highly unequal per-user time costs.
• Fairness trade-off: The NBS-based allocation distributes time costs more evenly across users but raises total travel time to 1028.3 minutes—a roughly 29% "cost of fairness" relative to the utilitarian optimum. This quantifies the efficiency–equity trade-off under fixed total capacity.

Subsidy intervention

To close the gap between the decentralized equilibrium and the NBS allocation without full centralization, the authors design a per-unit capacity subsidy computed by an outer-loop iterative search at the regulatory level: subsidies are adjusted until the induced Nash equilibrium converges to balanced travel times across stations. The subsidy lowers the effective marginal cost of capacity expansion, redirecting investment toward less accessible stations. Two effects follow: congestion at the most accessible stations is mitigated, and customer flows redistribute so that travel-time disparities across groups shrink, moving the market outcome toward the NBS allocation. The authors report this occurs with only a modest sacrifice of overall market efficiency, though they do not provide a precise numerical bound on the efficiency loss in the intervention scenario—an omission worth noting when interpreting the headline claim that inequities can be reduced "without significant efficiency loss."

Limitations and open questions

The paper concedes several substantive limitations. First, the fairness definition itself is contestable: the choice of disagreement point (benchmark) for the NBS materially affects outcomes, and alternative criteria—parity-based measures, Max–Min objectives—are not compared. Second, the model assumes customer homogeneity within each station's catchment; incorporating demographic data to represent heterogeneous choice patterns and group-specific disadvantage is left to future work. Third, the single OD-pair formulation abstracts away network coupling across OD pairs, and the linear congestion function is a simplification of queuing dynamics. Finally, the framework has not been validated against real-world charging data; all results derive from a stylized simulation with four stations and 100 customers, so the scalability of both the diagonalization algorithm and the subsidy search to realistic market sizes remains untested.

Conclusion

This paper contributes a tractable bi-level equilibrium framework linking CPO pricing/capacity competition to distributional outcomes in EV charging access, and demonstrates—within a stylized setting—that a calibrated capacity subsidy can shift a profit-driven Nash equilibrium toward an NBS-fair allocation at bounded efficiency cost. Its principal value for policymakers is methodological: a quantitative procedure for computing intervention levels rather than a prescription of specific subsidy values. The strength of its conclusions is correspondingly bounded by the homogeneity assumptions, the single-dimensional fairness metric, and the absence of empirical validation, all of which define the immediate agenda for extending this line of work.