Consider a first$-$price sealed bid auction between two bidders $($ties are broken with equal probability$).$ Each bidder may have a high valuation of H $=10$ with a probability of $0\mathrm{.}6$ or a low valuation of L $=1$ on the object being auctioned with a probability of $0\mathrm{.}4.$ A bidder's valuation is her private information. $(1)$ Suppose that the bid of each player can only be $1$ or $10.$ Solve for the pure$-$strategy symmetric BNE $($that is$,$ regardless of identity, a bidder will use one bid when her type is L and another $($possibly the same$)$ bid when her type is H$).(2)$ Now suppose that each player can bid any non$-$negative real number. Show that there is no pure$-$strategy symmetric BNE.