as the averaged charging prices of the service providers over a long period of time. In practice, the service providers take turns to set the retail price in response to the prices of the competitors. Additionally, if some of the other factors change (i.e. consumer’s preference, crude oil price soaring, etc.), the existing equilibrium breaks and a new equilibrium must be computed using the same procedure.

$\mathbf{Theorem\;1}$ \[Strategy Decision Condition\]: Service provider $k$ will choose placement policy $l(l=1,2,3,\cdots,2^L)$ if the type space $\Theta_k$ falls into the hypervolume specified by $$\begin{aligned}
&\mathcal{H}(l)=\\
&\{\Theta_k\in \mathbb{R}_+^L:\Theta_k^{\textrm{T}}\left(S_{k,j}-S_{k,l}\right)-(\mathbb{E}R_{k,j}-\mathbb{E}R_{k,l})\\
&\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;+w(B_{k,j}-B_{k,l})>0;\forall j \neq l\},
\end{aligned}$$ where $S_{k,j}$ and $S_{k,l}$ denote the placement strategy $j$ and $l$, respectively. $\mathbb{E}R_{k,j}$ and $\mathbb{E}R_{k,l}$ denote the expected total revenue with deployment strategy $j$ and $l$, respectively.

Each service provider has $L$ location candidates, so there are $2^L$ different placement policies. The type space can be seen as an $L$-dimensional space, and $\Theta_k=[\theta_{1,k},\theta_{2,k},\cdots,\theta_{L,k}]^{\textrm{T}}$ represents a point in this space.

By Equation (\[obj\]), strategy $l$ is optimal if $$\begin{aligned}
&\mathbb{E}[R_{k,l}]-\Theta_{k}^{\textrm{T}}S_{k,l}-wB_{k,l}>\mathbb{E}[R_{k,j}]-\\
&\;\;\;\;\;\;\;\;\;\;\Theta_{k}^{\textrm{T}}S_{k,j}-wB_{k,j};(j=1,2,\cdots,2^L, j \neq l).
\end{aligned}$$ Rearranging the terms, we get $$\begin{aligned}
&\Theta_k^{\textrm{T}}\left(S_{k,j}-S_{k,l}\right)-(\mathbb{E}R_{k,j}-\mathbb{E}R_{k,l})+\\
&\;\;\;\;\;\;\;w(B_{k,j}-B_{k,l})>0;(j=1,2,\cdots,2^L, j \neq l),
\end{aligned}$$ where each inequality represents a hyperplane and the intersection of all the inequalities defines a hypervolume 