generated by the $M$ generators under the base power load scenario (without EV charging), and $\mathbf{P}_{\textrm{g}}^{\textrm{EV}}=[P_1^{\textrm{EV}},P_2^{\textrm{EV}},\cdots,P_M^{\textrm{EV}}]$ is the vector of active power with EV charging (i.e., base power load superposed by EV charging load). Similarly, $\mathbf{Q}_{\textrm{g}}^{\textrm{base}}=[Q_1^{\textrm{base}},Q_2^{\textrm{base}},\cdots,Q_M^{\textrm{base}}]$ is the vector of reactive power of the base load, and $\mathbf{Q}_{\textrm{g}}^{\textrm{EV}}=[Q_1^{\textrm{EV}},Q_2^{\textrm{EV}},\cdots,Q_M^{\textrm{EV}}]$ is the vector of reactive power with EV charging. For a specific power system, $\mathbf{P}_{\textrm{g}}^{\textrm{base}},\mathbf{P}_{\textrm{g}}^{\textrm{EV}},\mathbf{Q}_{\textrm{g}}^{\textrm{base}}$, and $\mathbf{Q}_{\textrm{g}}^{\textrm{EV}}$ can be calculated through solving the global power flow equations.

Spatial Competition and Optimal Placement in A Bayesian Game
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It is pivotal for firms to choose the right location and product to compete with rivals in the same industry. Business locations will affect business competition, and conversely intensive competition will affect how firms choose the appropriate locations. One question arises naturally is whether or not firms from the same industry like to cluster their stores. There are some classical literature on spatial competition, e.g. Hotelling’s location model [@hotelling] and Salop’s circle model [@outside2]. Firms have incentives for both clustering and separation. On one hand, firms prefer clustering so that they can learn from each other on how to improve manufacturing and research productivity [@glaeser]-[@shaver], and learn demand from each other to reduce the cost 