Considering a non-cooperative game, there are $M$ players, the strategy of player $i$ ($i\in[1,2,\cdots,M]$) is $x_i \geq 0$, the utility function $u_i$ of $i$ is \begin{equation} u_i=\frac{a_i x_i}{\sum_{j=1}^M a_j x_j}R-bx_i, \end{equation} where $a_i>0$, $b>0$, $R>0$ are given coefficients.
How to verify the NE in this game is unique?