optimal bid strategy for uniform distribution

Question

Ten players take part in the following auction for a $\$$100 project from some company. If some player $i$ wins, the company will pay him his bid $b_i$. The ten players submit bids simultaneously, and the highest score wins the prize.The bids are given by \begin{align} b_i=100(1+x_i) \end{align} where $x_i\in (0,0.2)$. The score of each player can be calculated in the following rules. Firstly, calculate the average value of \begin{align} \bar{x}=\frac{1}{10}(x_1+x_2+\cdots+x_{10}) \end{align} Secondly, the bids that deviate $1/4$ of the average value will be eliminated, \begin{align} \frac{|x_j-\bar{x}|}{\bar{x}}\geq \frac{1}{4} \end{align} Thirdly, we calculate the average value of the remained bids, \begin{align} \bar{x'}=\frac{1}{m}\sum_{a=1}^mx_a \end{align} Finally, the final score is determined by the following, \begin{align} S= \left\{ \begin{aligned} &100-50\frac{|x_j-\bar{x'}|}{\bar{x'}},\,\,\,\,\,\, x_j<\bar{x'}\\ &100-100\frac{|x_j-\bar{x'}|}{\bar{x'}},\,\,\,\,\,\, x_j>\bar{x'} \end{aligned} \right. \end{align} W want to know the optimal bid. Is this the standard question in Nash's theory? I am not familiar with Nash's theory.