## 3 Results
### Model Calibration  
The proposed model is calibrated with the result of the IMT auction in 2018 in South Korea. As mentioned in Section 3.1, the auction was devised to sell 28 generic spectrum blocks at 3.5 GHz bandwidth (i.e., 3420-3700 MHz) to three major telecommunication companies. The starting price of the auction was $2348.76 million (i.e., $83.88 million per block). The auction continued until it identified the price where all 28 spectrum blocks were allocated to the three companies. As a result, at the 9 th round, companies A, B, and C purchased 10 blocks, 10 blocks, and 8 blocks, respectively. The total contract price was $2651.03 million (see Table 3).  
In fact, Company A and Company C paid additional costs for the potential to expand their spectrum blocks in the future by occupying both ends of the IMT spectrum blocks. To calibrate the proposed simulation model, we ignored the bidding price at Stage 2, because the value of the expendability could vary according to the company's strategy. The proposed model was able to complete Stage 1 at the 8 th round. Figures 7 and 8 show the trends of bids in terms of the bidding prices and the numbers of spectrum blocks over  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline MinBiddingPrice & Lower limit of total bidding price & \$2348.76 million \\ \hline BlockNum & Total number of spectrum blocks for sale & 28 blocks \\ \hline BuyUpperLimit & Purchasing upper limit & 10 blocks \\ \hline BuyLowerLimit & Purchasing lower limit & 8 blocks \\ \hline SuggestedPriceRate & Upper limit of a price increment ratio & 1\% \\ \hline Lambda\_1 (\(\lambda_{1}\)) & Price sensitivity of the Aggressive bidder & - \\  & agent & \\ \hline Lambda\_2 (\(\lambda_{2}\)) & Price sensitivity of the Moderate bidder & - \\  & agent & \\ \hline Lambda\_3 (\(\lambda_{3}\)) & Price sensitivity of the Conservative & - \\  & bidder agent & - \\ \hline FinalRound * & Round with the final decision & - \\ \hline FinalPrice * & Price with the final decision & - \\ \hline \hline \end{tabular}  
* Output parameters.  
\end{table}
Table 2: Simulation input and output parameters.  
multiple iterations. Before the 8 th round, all companies tried to maintain their bidding strategies. Because Company C is the Conservative bidder (Type 3) with the minimum competitiveness among the three bidders, it is beneficial to finish the auction when the bidding price is inexpensive. At the 8 th round, it tried to decrease its demand from 9 blocks to 8 blocks regarding its maximum capability (see Figure 8). Eventually, the auction was completed when the unit bidding price became $87.29 million per block (see Figure 7).  
The final bidding prices at Stage 1 for Company A, Company B, and Company C were $872.91, $872.91, and $698.33 million, respectively. R\({}^{2}\) of the simulation was 96.38%. Thus, we believed that the proposed model was successfully calibrated. From the calibration, values of \(\lambda_{1}\), \(\lambda_{2}\), and \(\lambda_{3}\) of 0.001, 0.07, and 0.22, respectively, were achieved. This implies that Company C has the most sensitivity to the bidding price change.  
Figure 8: Number of spectrum blocks over multiple rounds at Stage 1 (purple and blue lines are overlapped).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Category** & **Company A** & **Company B** & **Company C** \\ \hline Number of spectrum blocks & 10 & 10 & 8 \\ \hline Bandwidth (GHz) & 3.60–3.70 & 3.50–3.60 & 3.42–3.50 \\ \hline Bidding price at Stage 1 ($MM) & 856.54 & 856.54 & 685.23 \\ \hline Bidding price at Stage 2 ($MM) & 221.66 & - & 31.06 \\ \hline Contract price ($MM) * & 1078.20 & 856.54 & 716.29 \\ \hline \hline \end{tabular}  
* This is the sum of bidding price at Stage 1 and bidding price at Stage 2.  
\end{table}
Table 3: Results of the 3.5 GHz IMT spectrum auction in South Korea in 2018.  
Figure 7: Bidding price over multiple rounds at Stage 1 (purple and blue lines are overlapped).