# A Game-Theoretic Approach to Solve Competition between Multi-Type Electric Vehicle Charging and Parking Facilities

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## Abstract

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## 1. Introduction

- Planning level: issues such as charging pile deployment, electrical infrastructure construction, and vehicle charging scheduling arrangements have been studied.
- Economic level: the economic benefits of vehicle-to-grid (V2G) technology, the income of electric vehicle parking lots, and government support subsidies are studied.

- The competition and pricing strategy between parking/charging decks is studied with the local charging service platform as the main body to guarantee the optimal pricing strategy at the Nash equilibrium point;
- The paper applies the game theory principles to study the competitive relationship among parking platforms in order to maximize revenues, explains the nature of the problem using a special non-cooperative Bertrand game theory model, and provides an effective solution based on Nikaido–Isoda equations;
- EVs are divided into three groups according to price sensitivity with the quantified responses of different groups of customers through the experimental data, which simulate the customer behavior when the parking decks adopt different pricing strategies, and we obtain the experimental results for verification.

## 2. Problem Formulation

- The initial conditions of all parking/charging decks in the game theory model are the same, including electricity costs, parking fees, geographical advantages, etc.
- The game theory model uses the relaxation algorithm and Nikaido–Isoda function in the iterative process. The Nikaido–Isoda function is used to iteratively update the pricing strategy until the conditions are met to end the iterative process.
- The model will eventually reach an equilibrium point. Under the condition that other parking/charging decks keep their pricing strategies unchanged, no matter how this deck changes its strategy, it cannot continue to improve its own revenue.

#### 2.1. Parking

#### 2.2. Charging

#### 2.3. Charging Constraints of Electric Vehicles

#### 2.3.1. Constraint of Charging Demand

#### 2.3.2. Constraint of Dynamic Grid

## 3. Game Theory and Solution

#### 3.1. Game Theory Definition and Concepts

#### 3.2. Nikaido–Isoda Function

#### 3.3. Relaxation Algorithm

## 4. Numerical Results

#### 4.1. Experiment Settings and Condition Configuration

#### 4.2. Case Study

#### 4.2.1. Check of Convergence

#### 4.2.2. Evaluate Customer Influences

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**The charging price, parking fee, and total revenue after the number of SC customers in deck 6 was reduced to zero.

**Figure 5.**The charging price, parking fee, and total revenue after the number of LSC customers in deck 6 was reduced to zero.

**Figure 6.**The charging price, parking fee, and total revenue after the number of LC customers in deck 6 was reduced to zero.

**Figure 7.**The electricity price, parking fee, and total revenue after halving the number of SC customers in all decks and including them in Group LC.

**Figure 8.**The electricity price, parking fee, and total revenue after halving the number of SC customers in all decks and including them in Group LSC.

**Figure 9.**The electricity price, parking fee, and total revenue after reducing all LC customers in all decks and including them in Group LSC.

**Figure 10.**The electricity price, parking fee, and total revenue after halving the number of LSC customers in all decks and adding them to Group LC.

Customer Categories | Description | Whether Sensitive to Parking Price | Whether Sensitive to Charging Price | Examples |
---|---|---|---|---|

Loyalty customers (LC) | Consists of loyal customers who spend the same amount time charging on a fixed deck each day. | No | No | Customers who live or work locally and do not care about financial expenses. |

Less-sensitive customers (LSC) | Consists of customers who choose the same deck each day, but whose charging duration varies with the charging price. | Yes | No | Customers who live or work locally, care about financial expenses, and care more about convenience between economy and convenience. |

Sensitive customers (SC) | Consists of customers who use variable charging decks and have variable charging durations whose choices are influenced by both the price of the ${\mathrm{i}}_{\mathrm{th}}$ deck and the average price of all other decks. | Yes | Yes | Passing customers who are willing to spend time on economic planning. |

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**MDPI and ACS Style**

Jiang, M.; Chen, T.; Gao, C.; Ma, R.; Su, W.; Kavousi-Fard, A.
A Game-Theoretic Approach to Solve Competition between Multi-Type Electric Vehicle Charging and Parking Facilities. *World Electr. Veh. J.* **2023**, *14*, 59.
https://doi.org/10.3390/wevj14030059

**AMA Style**

Jiang M, Chen T, Gao C, Ma R, Su W, Kavousi-Fard A.
A Game-Theoretic Approach to Solve Competition between Multi-Type Electric Vehicle Charging and Parking Facilities. *World Electric Vehicle Journal*. 2023; 14(3):59.
https://doi.org/10.3390/wevj14030059

**Chicago/Turabian Style**

Jiang, Meihui, Tao Chen, Ciwei Gao, Rui Ma, Wencong Su, and Abdollah Kavousi-Fard.
2023. "A Game-Theoretic Approach to Solve Competition between Multi-Type Electric Vehicle Charging and Parking Facilities" *World Electric Vehicle Journal* 14, no. 3: 59.
https://doi.org/10.3390/wevj14030059