As China’s electricity market is facing many problems, the research on power producer’s bidding behavior can promote the healthy and sustainable development of China’s electricity market. As a special commodity, the “electricity” possesses complicated production process. The instable market constraint condition, nonsymmetric information, and a lot of random factors make the producer’s bidding process more complex. Best-response dynamic is one of the classic dynamic mechanisms of the evolutionary game theory, which applies well in the repeated game and strategy evolution that happen among a few bounded rational players with a quick learning capability. The best-response dynamic mechanism is employed to study the power producer’s bidding behavior in this paper, the producer’s best-response dynamic model is constructed, and how the producers would engage in bidding is analyzed in detail. Taking two generating units in South China regional electricity market as the example, the producer’s bidding behavior by following the producer’s best-response dynamic model is verified. The relationships between the evolutionarily stable strategy (ESS) of power producer’s bidding and the market demand, and ceiling and floor price as well as biding frequency are discussed in detail.
In the 1970s, when ecologists Maynard Smith and Price studied the ecology evolution phenomenon, they combined the biological evolutionism with the game theory and then came up the theory of evolutionarily stable strategy (ESS) [
When it comes to group decision-making, the player often observes others firstly and then learns from the game history to adjust his game strategy. The key point of evolutionary game theory is to identify the strategy adjustment path. Currently, there are three types of evolutionary decision-making mechanisms: the mechanism based on the best-response dynamic and replicate dynamic model, the mechanism based on random process or swarm intelligence optimization algorithm, and the mechanism based on neural network and reinforcement learning. Among those, the best-response dynamic model and the replicate dynamic model based on biological evolution are the most commonly used dynamic decision-making mechanisms [
Since the implementation of the
Although China’s electricity market reform has made some achievements, there still remain many problems. China’s top five large-scale power generation groups and some independent power generation companies with considerable size have initially formed the oligopolistic competitive pattern on the power generation side, but the regional electricity markets located in North China, Northeast China, Northwest China, East China, and Central China are just established and currently do not have full-fledged trading rules or settlement mechanisms. Besides, some serious problems have emerged at some regional markets, and even some on-going pilot projects have been interrupted. To pursue greater profits, all the power generation companies have motives to increase the electricity price at the regional electricity market, which will naturally lead to the strategic bidding of many power generation companies. This will bring harm to the safe operation of power grid as well as the price stability [
Because of the specificity of electricity as a commodity and the complexity of its production, the traditional game model cannot be applied well in the electricity market. Meanwhile, the instable market constraints, information asymmetry, and plenty of random factors affect the biding process, which make this issue more complex. Therefore, in this paper, according to the actual situation of China’s electricity market, the best-response dynamic model of oligopolistic power producer’s bidding is constructed based on the assumption that all producers have bounded rationality, and then the relationships between the evolutionarily stable strategy (ESS) of power producer’s bidding and the market demand and ceiling and floor price as well as biding frequency are discussed.
The paper is organized as follows: Section
The best-response dynamics is usually applied in the adjustment process of a repeated game among players who have rapid learning ability and bonded rationality. The rapid learning ability means that the players can make accurate postevaluation on the results of different strategies and then adjust their strategies accordingly although their abilities of judgment and foresight are a bit poor under the complicated situation. Therefore, when the former gaming result is given, each player can identify the best-response strategy compared with the former strategies adopted by other players.
According to the theory of Fudenberg and Levine, the best-response dynamic equation of player
Equation (
The random best-response dynamic model of producer’s bidding adjustment was proposed by Larson and Salant, the mechanism of which is that each producer tends to adjust his bidding strategy according to the competitors’ previous bidding strategies [
Suppose that
Some assumptions need to be made when performing the best-response dynamic model of power producer’s bidding. Suppose that there are
The producer
If a producer’s bidding price is lower than or equal to the clearing price, he can sell out all the declaratory power generation at the unified clearing price. However, if the producer’s bidding price is higher than the clearing price, his power generation will not be sold out, and then his profit will be equal to zero. The profit function of producer
According to [
After one round of bidding, the producer
Figure
The best-response dynamic process of producer’s bidding price.
Evolutionarily stable strategy (ESS) is an important concept in the game learning theory, which reflects the achieved equilibrium state after the best-response dynamic adjustment process. According to the connotation of ESS, the ESS of best-response dynamic adjustment on producer’s bidding price is as follows.
Suppose
If the producer’s profit
An evolutionarily stable strategy should meet the following requirements. The proportion of individuals adopting this strategy keeps constant, which means the value of This stable state must have robustness against the slight disturbance, which means the system can automatically recover to the evolutionarily stable state from the unstable state.
Therefore, the ESS The profit of producer Even though there exists a slight bidding strategy disturbance
The best-response dynamic model applies well in the gaming behavior that involves a few players who have strong learning ability. Meanwhile, the producers in the oligopolistic electricity power have the characteristics of small number, large scale, and strong information searching-analyzing-processing capability. By learning the historical market information and predicting the development trend, the producer can estimate both the competitors’ bidding prices and profits and then acts properly against the competitors’ bidding strategies. Therefore, the best-response dynamic model of power producer’s bidding can be used to study the bidding behavior of oligopolistic producer in the electricity market and the price bidding trend.
Suppose that there are two exact oligopolistic producers in one regional electricity market. Due to the symmetry, this paper only needs to study one oligopolistic producer
According to the above suppositions and the best-response dynamic model, the profit of producer
According to (
Equation (
Suppose that
The relationship between ESS (
In Figure
Just as shown in Figure
Meanwhile, the floor price can also affect the producer’s bidding strategy, but its effect is quite special: when the market demand is small (
Suppose that the initial bidding price of producer
Then, we can get
When the marker demand, ceiling price, floor price, and producer’s initial bidding price are given, the relationship between bidding frequency and ESS can be discussed. Suppose
The relationship between ESS of producer’s bidding and bidding frequency is shown in Figure
The relationship between ESS of producer’s bidding and bidding frequency (
Moreover,
Two competitive generating units from South China regional electricity market are selected. Considering the limitation of essential data, the sample range includes 24 time points of relevant indicators of generating units. The cost and production capacity of these two competitive generating units are listed in Table
The cost and production capacity of two competitive generating units.
Cost |
Production capacity |
|
---|---|---|
(RMB/MWh) | (MWh) | |
Generating unit number 1 in power plant TG | 378 | 432000 |
Generating unit number 1 in power plant DG | 289 | 432000 |
The declaratory electricity power and limited prices.
Time points | The declaratory electricity power ( |
Ceiling price for sale ( |
Floor price for buy-in ( |
---|---|---|---|
1 | 113360 | 540 | 180 |
2 | 121410 | 540 | 180 |
3 | 106820 | 540 | 180 |
4 | 210360 | 540 | 180 |
5 | 210360 | 540 | 180 |
6 | 247070 | 555 | 184 |
7 | 227280 | 555 | 184 |
8 | 227310 | 555 | 184 |
9 | 221320 | 555 | 184 |
10 | 254560 | 555 | 184 |
11 | 228620 | 555 | 184 |
12 | 243200 | 555 | 184 |
13 | 221520 | 555 | 184 |
14 | 211350 | 555 | 184 |
15 | 210950 | 555 | 184 |
16 | 264220 | 555 | 184 |
17 | 265000 | 555 | 184 |
18 | 276130 | 555 | 184 |
19 | 235870 | 555 | 184 |
20 | 235870 | 555 | 184 |
21 | 254560 | 555 | 184 |
22 | 244030 | 555 | 184 |
23 | 246280 | 555 | 184 |
24 | 286580 | 555 | 184 |
The declaratory electricity price of generating units.
Power plant TG | Declaratory electricity price (RMB/MWh) | Power plant DG | Declaratory electricity price (RMB/MWh) |
---|---|---|---|
1 | 245 | 1 | 261 |
2 | 430 | 2 | 270 |
3 | 480 | 3 | 270 |
4 | 500 | 4 | 268 |
5 | 540 | 5 | 275 |
6 | 550 | 6 | 277 |
7 | 530 | 7 | 272 |
8 | 538 | 8 | 289 |
9 | 545 | 9 | 308 |
10 | 524 | 10 | 308 |
11 | 546 | 11 | 316 |
12 | 546 | 12 | 316 |
13 | 546 | 13 | 316 |
14 | 538 | 14 | 315 |
15 | 548 | 15 | 316 |
16 | 548 | 16 | 315 |
17 | 549 | 17 | 319 |
18 | 549 | 18 | 324 |
19 | 551 | 19 | 321 |
20 | 551 | 20 | 332 |
21 | 551 | 21 | 332 |
22 | 524 | 22 | 323 |
23 | 524 | 23 | 333 |
24 | 524 | 24 | 320 |
In the region electricity market, the electricity demand fluctuates over time, which is shown as the increase or decrease in the declaratory electricity power at different periods of time. Just as shown in Figure
The relationship between market demand and the producer’s bidding strategy.
When the ceiling price is set at a low level, the producers will offer a low price, which makes the overall bidding price become low; but when the ceiling price is set at a high level, the producer’s optimal bidding price will rise. So, the ceiling price could not inhibit the motive of producer to raise the electricity price, which is shown in Figure
The relationship between ceiling price and producer’s bidding strategy.
The floor price will also affect the producer’s bidding strategy. Due to the fact that the sample data is selected from the regional electricity market, its market demand is relatively small compared with the overall market demand. So, the multiple
The relationship between floor price and producer’s bidding strategy.
According to the above analysis, the ESS of producer’s bidding will go up with the increase of the bidding frequency and eventually converges into the bidding price strategy expressed as
The relationship between ESS and bidding frequency.
The producer’s bidding strategy based on the best-response dynamic mechanism is studied and the best-response dynamic model of producer’s bidding behavior is constructed in this paper. Taking two generating units in South China regional electricity market as the example, the monopolistic producer’s bidding behaviors are empirically studied, and some conclusions are drawn as follows. With the increase of electricity power demand, the oligopolistic producer tends to raise his bidding price. If the bidding behavior cannot be restrained, when the market demand goes near the producer’s supply capacities, all producers will raise the bidding price to a very high level. This conclusion has been proved by the power crisis in California. The ceiling price has some certain effects on inhibiting the motive of producers to raise the electricity price, and the producer’s overall bidding price will go with the ceiling price. This implies that setting reasonable celling price should not only consider how to keep the producers away from raising the bidding price, but also consider how to motive the producers in terms of profit. When the electricity power demand is small, the floor price can play a role in avoiding the virulent price bidding behavior of producers. But when the electricity demand becomes large, the floor price will not work. When the number of market trading increases, the producer’s bidding frequency will increase, and the producer can gradually adjust his bidding price by learning market information and analyzing competitors’ bidding strategies until the maximum profit can be obtained.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This study is supported by the National Natural Science Foundation of China (Project no. 71373076) and the Humanities and Social Science project of the Ministry of Education of China (Project no.11YJA790217). The authors are grateful to the editor and two anonymous reviewers for their suggestions in improving the quality of the paper.