are interested in investigating how the different charging services compete with each other in choosing locations and prices. Each service provider can run multiple charging stations. At each planning stage, service providers select some charging stations from a given set of candidates, denoted as $\mathcal{I}=\{1,2,3\cdots,L\}$. The set of EVs is denoted as $\mathcal{E}=\{1,2,3,\cdots,N\}$.

The Profit of EV Charging
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   Charging Method   Nominal Supply Voltage(Volts)   Max Current (Amps)   Time from fully depleted to fully charged
  ----------------- ------------------------------- -------------------- -------------------------------------------
       Level 1             120 vac, 1-phase                 12 A                         16-18 hours
       Level 2          208 to 240 vac, 1-phase             32 A                          3-8 hours
       Level 3              600 vdc maximum            400 A maximum                less than 30 minutes

We assume that service providers run the charging stations like “chain stores", so that charging stations affiliated with the same service provider have the same retail charging price. The charging stations purchase the electricity from the wholesale market at the locational marginal price (LMP). In a deregulated electricity market (like PJM, NYISO, NEISO, MISO, ERCOT, California ISO in USA, the New Zealand and Singapore markets), LMP is computed at every node (bus) by the market coordinator. LMP primarily consists of three components: system energy price, transmission congestion cost, and cost 