## 5 Discussion of Simulations and Results
### Implementing a GDCAC-Based Approach on the Test System
When we make state variable 1 and 2 change randomly within interval [0, 20] MW and [0, 30] MW, respectively, in each iteration, the Nash indices obtained after 20000 iterations in 10 state samples are listed in Table 4.  
From Table 4 it can be verified, to a certain extent, that the generalization ability of our proposed GDCAC-based EM approach can make the obtained strategies of all participants in face of any state point within the continuous space \(\{(x_{1},x_{2})|x_{1}\in[0,\,20],x_{2}\in[0,\,30]\}\) reach NE based on those finite and discrete sample state points occurred during the 20,000 iterations. Figure 6 shows NRGenCO 2's bidding strategy (\(k_{\text{g2}}\)) in the face of any state point within \(\{(x_{1},x_{2})|x_{1}\in[0,\,20],x_{2}\in[0,\,30]\}\) after 20,000 iterations. From Figure 6, we can see that after 20,000 iterations, no matter the increase in the power output level of any one of the two wind farms, the value of NRGenCO2's bidding strategy will increase accordingly. That is because increasing the power output levels of the two wind farms could cause congestion in the transmission lines connecting bus 1 to 2 and connecting bus 12 to 13, which limits the increase in NRGenCO2's dispatched power output. Gradually, NRGenCO2, through repeatedly interacting with the EM environment over 20,000 iterations, learns that by increasing the value of its bidding strategy so as to maintain or increase the LMP level in bus 2, it could make comparatively more profit. Therefore, taking transmission congestion into account, some NRGenCOs' market powers could be enhanced while increasing the wind power output. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**State Sample** & **(12, 24)** & **(18, 27)** & **(10, 30)** & **(11, 22)** & **(6, 24)** \\ \hline Nash index & \(1\) & \(1\) & \(1\) & \(1\) & \(1\) \\ State sample & (4, 11) & (8, 23) & (19, 27) & (18, 16) & (20, 20) \\ Nash index & \(1\) & \(1\) & \(1\) & \(1\) & \(1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Nash indices in 10 random state samples after 20,000 iterations. Figure 5: Nash index during the learning iterations of the proposed GDCAC method when the state vector is (20, 30) MW. Figure 7 shows the NRGenCO2's bidding strategy (\(k_{\text{g2}}\)) corresponding to the state space after 20,000 iterations in the case of ignoring all transmission lines' congestions in this test system. From Figure 7, we see that after 20,000 iterations, no matter the increase in the power output level of any one of the two wind farms, the value of NRGenCO2's bidding strategy will decrease accordingly. In fact, other NRGenCOs' bidding strategies are also subject to a similarly changing law. Therefore, if we ignore the transmission congestion in the test system, NRGenCOs' market powers would be weakened while increasing the wind power output. Figure 8 shows the average LMP of 30 buses (AVLMP) corresponding to the state space after 20,000 iterations. Figure 6: Bidding strategy of NRGenCO2 corresponding to the state space after 15,000 training and 5000 decision-making iterations (considering transmission line congestion constraint). Figure 7: Bidding strategy of NRGenCO2 corresponding to the state space after 15,000 training and 5000 decision-making iterations (ignoring transmission line congestion constraint). Figure 8 reveals that, although the market power of some NRGenCOs could be enhanced if the transmission capacities in some transmission lines were insufficient, the obtained AVLMP after 20,000 iterations decreases while increasing the wind power output level. We think there may be two main reasons for the phenomenon in Figure 8 that need to be further verified: (1) the marginal cost of the wind farm is significantly lower than that of all NRGenCOs (so we assume it is zero), which in turn pulls down the overall LMP level; (2) the increase in wind power output can reduce most agents' market power and increase the degree of competition in the whole EM.