# Price Strategy Analysis of Electricity Retailers Based on Evolutionary Game on Complex Networks

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Research Background and Contribution

#### 1.2. Literature Review

#### 1.2.1. Evolutionary Game

#### 1.2.2. Complex Network

#### 1.2.3. User’s Switching Behavior

#### 1.2.4. Research Hypothesis

**Hypothesis**

**1**

**(H1).**

**Hypothesis**

**2**

**(H2).**

**Hypothesis**

**3**

**(H3).**

**Hypothesis**

**4**

**(H4).**

## 2. Analysis of Complex Network Characteristics of Electricity Retailers

## 3. Analysis of User Switching Behavior

#### 3.1. Scene Description

#### 3.2. User Revenue Function

#### 3.3. Electricity Retailer Revenue Function

#### 3.3.1. Sales Revenue in the Retail Electricity Market

- Electricity sales revenue from contract

- Electricity sales revenue from participating in bidding transaction

#### 3.3.2. Electricity Purchase Cost of Electricity Retailer

#### 3.3.3. Revenue of Electricity Retailer

#### 3.4. Market Share Function

**b**is a symmetric matrix, and since the main diagonal elements of matrix

**b**are not zero, matrix

**b**is invertible. Let ${b}^{-1}=\beta $, we know that

**β**is also a symmetric matrix, that is, ${\beta}_{i,j}={\beta}_{j,i}$, and the diagonal element is denoted as ${\beta}_{i}$. Thus, Equation (7) can be written in the following form.

## 4. Evolutionary Game Bidding Model for Electricity Retailers

#### 4.1. Evolutionary Game Theory

- Interactivity. On the one hand, the price strategy selected by the electricity retailer during the game may have a great impact on the opponent’s price strategy. On the other hand, the interests of each participant interact with other participants through the market clearing process, and the electricity retailer may also be affected by the bids of other electricity retailers.
- Adaptability. Electricity retailers adapt to their own price strategies and those of other retailers, they learn and adjust their own quotations over time and update their estimates of other retailers’ price strategies based on historical information and newly released information.

#### 4.2. Evolutionary Game Model of Electricity Retailers Based on Complex Network and User Switching Behavior

#### 4.2.1. Model Assumptions

- There are N electricity retailers in the retail electricity market, and $2\le N\le \infty $, that is, the number of electricity retailers is limited, and no electricity retailers exit the market, and there may be new electricity retailers entering the market. There will be a BA scale-free network structure among the electricity retailers.
- The strategy of all electricity retailers is a set of retail price strategies $S=\{{s}^{\mathrm{h}},{s}^{\mathrm{l}}\}$, where ${s}^{\mathrm{h}}$ indicates high price strategy, and ${s}^{\mathrm{l}}$ indicates low price strategy.
- When electricity retailers choose game opponents, due to limited information access, they cannot establish contact with each electricity retailer in the network, but choose neighboring entities to play the game.
- Electricity retailers are in a state of bounded rationality during the bidding game, and the probability of selecting a strategy is related to the expected return of the strategy.
- In order to facilitate the calculation and make the game system reach a relatively stable state as soon as possible, it is assumed that all electricity retailers use the same rule to update the strategy. When the strategy is updated, the electricity retailer only determines the strategy to be adopted in the next game according to the results of this game.

#### 4.2.2. Model Building

**S**denote the strategy of the electricity retailer, $S=\left(0,1\right)$ indicates that the electricity retailer adopts a low price strategy, $S=\left(0,1\right)$ indicates that the electricity retailer adopts a high price strategy, then the total revenue ${U}_{i}$ of each round of the game of the retailer i in the network is the sum of the revenue obtained from the game with all neighbors, as shown in the following formula.

#### 4.2.3. Strategy Update Rule

#### 4.2.4. Network Evolutionary Game Algorithm

- Step 1:
- Construct the BA scale-free network of the electricity retailers and initialize the parameters of the game system at $t=0$.
- Step 2:
- According to Equations (2)–(5), the revenue parameters of the electricity retailer i under different strategy combinations are calculated.
- Step 3:
- The calculated revenue and the price strategies of all neighbors of the electricity retailer i are substituted into Equation (11) to obtain the corresponding total revenue.
- Step 4:
- Electricity retailer compares revenue with neighboring nodes in a random probability. When the revenue of electricity retailer i is greater than that of neighboring nodes, it does not make any change, when the revenue of the electricity retailer i is less than that of the neighboring nodes, it learns the strategy of neighboring nodes in the network according to the strategy update rules set in Equation (12), and then imitates and improves its strategy.
- Step 5:
- Loop steps 2, step 3 and step 4 at $1<t<T$, and execute loop until the specified evolution time T.

## 5. Case Analysis

#### 5.1. Parameter Settings

^{2}h/USD. In the wholesale market, the parameter of wholesale electricity price A = 30 USD/MWh, ζ = 0.00045 USD/(MW)

^{2}h. The overconfidence level ${\theta}_{i}$ of the electricity retailer is 10, and the environmental noise $\tau $ is 10

^{6}.

#### 5.2. Results Analysis

#### 5.2.1. The Impact of Retail Contract Transaction on Game Evolution

#### 5.2.2. The Impact of User Switching on Game Evolution

^{2}h/USD, [−20, −2] (MW)

^{2}h/USD and [−40, −20] (MW)

^{2}h/USD. The evolutionary game process and the average network revenue results of electricity retailers in the final game under different switching parameters are shown in Figure 4 and Table 3, respectively.

#### 5.2.3. The Impact of the Level of Overconfidence on Game Evolution

## 6. Discussions

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Electricity Retailer j | High Price s^{h} | Low Price s^{l} | |
---|---|---|---|

Electricity Retailer i | |||

high price s^{h} | $({\pi}_{\mathrm{R}}^{i1},{\pi}_{\mathrm{R}}^{j1})$ | $({\pi}_{\mathrm{R}}^{i2},{\pi}_{\mathrm{R}}^{j2})$ | |

low price s^{l} | $({\pi}_{\mathrm{R}}^{i3},{\pi}_{\mathrm{R}}^{j3})$ | $({\pi}_{\mathrm{R}}^{i4},{\pi}_{\mathrm{R}}^{j4})$ |

Contract Electricity ${\mathit{q}}_{\mathit{i}}^{\mathit{c}}$ | The Average Network Revenue (USD) | |
---|---|---|

30 Nodes | 90 Nodes | |

[0, 300] MWh | 1.04 × 10^{5} | 9 × 10^{4} |

[300, 600] MWh | 9.2 × 10^{4} | 7.4 × 10^{4} |

[600, 900] MWh | 4.9 × 10^{4} | 3.8 × 10^{4} |

Switching Parameter ${\mathit{\beta}}_{\mathit{i},\mathit{j}}$ | The Average Network Revenue (USD) | |
---|---|---|

30 Nodes | 90 Nodes | |

[−2, 0] (MW)^{2}h/USD | 1.20 × 10^{5} | 1.05 × 10^{5} |

[−20, −2] (MW)^{2}h/USD | 1.26 × 10^{5} | 1.19 × 10^{5} |

[−40, −20] (MW)^{2}h/USD | 1.54 × 10^{5} | 1.52 × 10^{5} |

Overconfidence Levels ${\mathit{\theta}}_{\mathit{i}}$ | The Average Network Revenue (USD) | |
---|---|---|

30 Nodes | 90 Nodes | |

[5, 10] | 1.20 × 10^{5} | 1.07 × 10^{5} |

[10, 30] | 1.19 × 10^{5} | 1.05 × 10^{5} |

[30, 50] | 9.24 × 10^{4} | 8.56 × 10^{4} |

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## Share and Cite

**MDPI and ACS Style**

Xie, X.; Ying, L.; Cui, X.
Price Strategy Analysis of Electricity Retailers Based on Evolutionary Game on Complex Networks. *Sustainability* **2022**, *14*, 9487.
https://doi.org/10.3390/su14159487

**AMA Style**

Xie X, Ying L, Cui X.
Price Strategy Analysis of Electricity Retailers Based on Evolutionary Game on Complex Networks. *Sustainability*. 2022; 14(15):9487.
https://doi.org/10.3390/su14159487

**Chicago/Turabian Style**

Xie, Xinyi, Liming Ying, and Xue Cui.
2022. "Price Strategy Analysis of Electricity Retailers Based on Evolutionary Game on Complex Networks" *Sustainability* 14, no. 15: 9487.
https://doi.org/10.3390/su14159487