## 2 Materials and Methods
### Agent-Based Simulation for the Design of a Spectrum Auction Policy
#### 2.3.1 Bidder Agents  
Figure 2 represents the decision-making process model of the auction bidder agents in the agent-based simulation. In Figure 2, the decision-making process of each agent consists of two states, namely an Idle state and a Decision state. In the Idle state, a bidder agent is preparing for the next round of an auction regarding its investment preference, which is influenced by budget (Budget). As mentioned in Section 2.2, the budget constraint is the most significant factor for the decision-making of a bidder [11]. In this stage, the agent evaluates alternatives in terms of the price increment and the number of spectrum blocks. Figure 1: Conceptual model of the proposed agent-based simulation approach for the clock auction. At the Decision state, the agent offer is a bid involving the auction price (Price) and the demand for spectrum blocks (NumOfBlocks). To model the decision-making behavior of an agent, this study adopts the exponential utility theory, which is widely adopted in the choice behavior modeling of a corporation or an individual [15]. This is because, as the price increases, the choice probability of a human (or a company) exponentially decreases. Thus, the acceptance rate at a certain suggested price of each agent follows Equation (5). Note that the government agency determines the suggested price based on the rule of Vickrey-nearest core pricing (see Section 2.2). \[y=\lambda exp\left(-\lambda\left(p_{suggested}/b\right)\right) \tag{5}\]  
where \(p_{suggested}\) is the suggested (or offered) price at each round, and \(b\) is the available (or investment) budget of a bidder agent. \(\lambda\) is the price sensitivity of each agent where \(0<\lambda<1\), and it is affected by the investment preference. Under the given \(\lambda\) and \(b\), as the suggested price (\(p_{suggested}\)) increases, the choice probability (\(y\)) decreases, due to the economic burden on the bidder. This implies that, as the suggested price increases, the demand in terms of the number of spectrum blocks should be reduced, because the total price of each bid is computed by multiplying the suggested price by the number of spectrum blocks. Suppose that \(L\) is the upper limit of demand referring to the maximum number of spectrum blocks bought by a single bidder. Then, Equation (6) represents the actual demand of spectrum blocks, which is influenced by the price sensitivity of each agent on the upper limit of demand on the spectrum blocks (i.e., \(L/\lambda\)). \[m=\left(\frac{L}{\lambda}\right)\lambda exp\left(-\lambda\left(p_{suggested} /b\right)\right)=L\cdot exp\left(-\lambda\left(p_{suggested}/b\right)\right) \tag{6}\]  
Eventually, Equation (6) enables the choice behavior of a bidder agent who tends to buy more spectrum blocks with low price sensitivity (\(\lambda\)) or at the cheap suggested price (\(p_{suggested}\)) to be modelled. The proposed ABS consists of three major agent types: (1) the Aggressive bidder (Type 1), (2) the Moderate bidder (Type 2), and (3) the Conservative bidder (Type 3). The Aggressive bidder is the most competitive company in terms of budget for the spectrum auction. To be more competitive by taking spectrum usage right, it has sufficient budget for the auction. On the other hand, the Conservative bidder is considered the least competitive company in terms of the auction budget. The Moderate bidder is between the Aggressive bidder and Conservative bidder in terms of the auction budget. It tends to maintain its current market share. The difference in decision-making between these three types of agents is determined by the parameter \(\lambda\) which is the price sensitivity of  
Figure 2: The decision-making process of auction bidder agents. each agent. Figure 3 reveals the pseudo code to compute \(m\) based on the three parameters (i.e., \(\lambda\), \(p_{suggested}\), and \(b\)) addressed in Equation (6). Figure 4 depicts how the number of spectrum blocks can vary under three different price sensitivity parameters (i.e., 0.01, 0.07, and 0.22).