## 2 Materials and Methods
### Agent-Based Simulation for the Design of a Spectrum Auction Policy
#### 2.3.2. Auction Environment Modeling  
The three agent types addressed in Section 2.3.1 participate in a spectrum auction in the simulation model consisting of multiple rounds. At each round, the model sends the information of the suggested price to all agents. According to the rule of CA, the suggested price cannot exceed an upper limit on the ratio of the price increment (i.e., SuggestedPriceRate). To consider the uncertainty involved in the suggested price, uniform distribution is used to determine the suggested price, which is between the selected price (\(p_{selected}\)) at the former round and the maximum price, considering the upper limit on a ratio of the price increment at the current round. For example, when the SuggestedPriceRate is 1% and the selected price at the former round is $2348.76 million, the suggested price at the current round is randomly selected from any value in the range $2348.76\(-\)2372.25 million. Note that the price choice in early rounds is arbitrary [30].  
In addition, after the first round, each bidder agent can offer two alternative prices (i.e., two bids). These two prices should be higher than the selected price at the former round, and lower than the suggested price at the current round [26]. Similar to the suggested price selection, uniform distribution is used to determine the two prices for each agent. However, the demand of spectrum blocks (\(m\)) is computed by Equation (3) under the two different prices. In this case, two bidding prices are used, instead of \(p_{suggested}\).  
Once all bids involving values of \(m\) are generated, the simulation model considers the bids in ascending order. However, according to the rule of CA addressed in Section 2.1, the model only considers the case in which the total value of \(m\) equals the number of the supplied spectrum blocks (\(M\)). If there is no such case, the bidding price and demand of spectrum blocks are determined by the rule addressed in Section 2.1. This complex calculation is modeled by the event module in AnyLogic 8.5.0. Figure 5 provides an overview of the developed simulation model.  
Figure 5 shows that the developed simulation environment includes multiple variables and parameters of ABS, while Table 1 addresses the major variables to illustrate the spectrum auction environment. In particular, since the CA requires multiple rounds to compare the current price (or suggested price) with the selected price, multiple variables are required. Also, all suggested prices should be sorted in ascending order for the selection of the minimum price (\(p_{min}\)). This is because the price should satisfy all bidders situations. If the maximum price is selected from the suggested prices, only some of the bidders with sufficient budget (e.g., the Aggressive bidder and the Moderate bidder) can buy the spectrum blocks. Note that the goal of the auction held by a government agency is to identify an appropriate value for the spectrum by allocating all blocks to bidders, without causing any harmful impact on a monopolistic market, as well as the public (i.e., the users of the IMT services). Section 3.1 will address additional parameters.  
Figure 5: An overview of the developed simulation model in AnyLogic 8.5.0.  
Figure 6 shows the selection logic from multiple bids involving price and demand (i.e., number of spectrum blocks). Once each agent offers its bid, the ABS collects the bids, and selects the bidding price (i.e., selected price, \(p_{selected}\)) at each round. The first round uses the minimum price suggested by the government agent (i.e., \(p_{min}\)). After that, the suggested price (\(p_{suggest}\)) is compared to all bid prices given by the agents. If the total demand equals the total number of spectrum blocks for sale, the function returns the selected bidding price (\(p_{selected}\)). Otherwise, the ABS computes a new suggested price for the next round. The CA continues until it finds a price where the total demand equals the total number of spectrum blocks for sale.