$3\mathrm{.}3$ Consider the bimatrix game that models the game $of$ chicken:

Two cars are headed toward each other $at$ a high rate $of$ speed. Each player has two

options: turn off, $or$ continue straight ahead. This game $is$ a macho game for reputation,

but leads $to$ mutual destruction $if$ both play straight ahead.

$(a)$ There are two pure Nash equilibria. Find them.

$(b)$ Verify $by$ using the definition $of$ mixed Nash equilibrium that the mixed strategy pair

$x^{*}=(\frac{3}{52},\frac{49}{52}),Y^{*}=(\frac{3}{52},\frac{49}{52})is$ a Nash equilibrium, and find the expected payoffs

$to$ each player.

$(c)$ Find the safety levels for each player.