policies of the competing players. Denote $f(S_{-k})$ as probability mass function (PMF) of the placement policies of the other players. The type space $\Theta_k=[\theta_{1,k},\theta_{2,k},\cdots,\theta_{L,k}]^{\textrm{T}}$ corresponds to the placement costs of all charging station candidates of service provider $k$. In this paper, we assume that a service provider knows its own type, but not the types of the other two competing players.

Let $\theta_{j,k}$ denote the placement cost for $j$-th charging station candidate of service provider $k$, which includes the charging equipment cost, installation fee, construction cost, land rental cost, etc. $\theta_{j,k}$ has i.i.d. uniform distribution.

Before proceeding to analyze the Bayesian game, we need the following assumptions.

$\mathbf{Assumption\;1}$: $f(S_{-k})$ is binomially distributed with parameter 0.5, *i.e.* $S_{-k}\backsim \textrm{Binomial}(2L, 0.5)$.

$\mathbf{Remark\;1}$: The distribution of $S_{-k}$ reflects player $k$’s conjecture on how other players will act during the game. Each player can form their conjectures about other players according to their beliefs about the competitors. For instance, a player may be risk neutral, risk aversion or risk seeking. For simplicity, we assume that $S_{-k}$ has a binomial distribution with parameter 0.5. However, the theoretical analysis can be applied to any other distribution of $S_{-k}$.

$\mathbf{Assumption\;2}$: All service providers in the market are 