3.2.2. Action Model

The simulation included passengers and drivers for each cell in the OD matrix and determined whether or not a match was feasible on the basis of the choice probability of passengers and drivers. Applying the method used by Wu et al. [34], passengers selected a price according to the surge according to a normal distribution. On the other hand, drivers applied choice probability according to a normal distribution with the weight of the centrality analysis outcome in accordance with their destination. Centrality analysis was applied to taxi operation data on the basis of 150 M links provided for Seoul Metropolitan City. The analysis was conducted using data from April to September of 2017 which were processed to generate OD data for each district (gu).

For the choice probability model of drivers and passengers, a surge of 1 (base fare of taxi) was applied by consulting the result of National Bureau of Economic Research(NBER, 2016) study [37]. In addition, the probability followed a cumulative normal distribution using the following equation:

$$\Phi(\mathbf{x}) = \int\_{-\infty}^{\mathbf{x}} N(0, 1)(\mathbf{x}) d\mathbf{x}.\tag{3}$$

*Electronics* **2020**, *9*, 1818

The choice probability models of passengers (Equation (4)) and drivers (Equation (5)) according to the surge are expressed below.

$$P\left(accept \middle| P\_{offer}\right) = \Phi\left(\frac{P\_{offer} - P\_{base}}{\sigma}\right) \times W\_{1\prime} \tag{4}$$

$$P(accept|P\_{offer}) = \Phi\left(\frac{P\_{base} - P\_{offer}}{\sigma}\right) \times \mathcal{W}\_2 + \left(\frac{T\_r C\_{outD}' \{N\_j\}}{T\_r C\_{inD}' \{N\_j\}}\right) \times \mathcal{W}\_3. \tag{5}$$

where *W*1 is the weight modifying the choice probability of passengers when surge = 1, *W*2 is the weight modifying the choice probability of drivers when surge = 1, *TrCoutDNj* is the out-degree centrality value of a specific time round (*Tr*), *TrCinDNj* is the in-degree centrality value of a specific time round (*Tr*), and *W*3 is the weight of the equity index allowing differentiation by region.
