The policeman Clouseau and the criminal Walter play a simultaneous$-$move game as indicated below in the game matrix. They can each choose to go to either Sergels torg or Bj$$rns tr$$dg$$rd$.$ If they go to the same place Clouseau catches Walter and if they don$$tWalter roams free. Clouseau prefers to make the arrest at Sergels torg $($he wants to impress a lady who works there$)$ and Walter would, if caught, prefer to be caught at Bj$$rns tr$$dg$$rd $($he then gains some street cred in the rough southern part of town$).$ What is the mixed$-$strategy Nash equilibrium of this game?

$($A$)$ Both players go to Sergels torgwith $50\%$ probability.

$($B$)$ Clouseau goes to Sergels torg for sureand Walter goes to Bj$$rns tr$$dg$$rdfor sure.

$($C$)$ Both players go to Sergels torgwith $(100/3)\%$ probability.

$($D$)$ Clouseau goes to Sergels torg with $(100/3)\%$ probability and Walter goes to Bj$$rns tr$$dg$$rd with $(100/3)\%$ probability.

$($E$)$ This is a trick question, there is no mixed$-$strategy Nash equilibrium.$\backslash$table$[[,,$Walter$],[,,$Sergels torg,Bj$$rns tr$$dg$$rd$],[$Clouseau$,$Sergels torg,$200,0,0,100],[$Bj$$rns tr$$dg$$rd$,0,100,100,50]]$