Problem $1.(10$ points$)$ Two drivers simultaneously approach an intersection from different

directions. Each driver can either stop $($S$)$ or continue $($C$).$ The drivers$$ preferences are given

in the following payoff matrix:

S C

S $1,11,2$

C $2,10,0$

where the parameter in $(0,1)$ reflects each driver$$s aversion to being the only one who stops.

$1.$ Find the pure strategy Nash equilibria of this game.

$2.$ Find the mixed strategy Nash equilibrium of this game.

$3.$ In the mixed strategy Nash equilibrium what is the likelihood of both drivers continuing

$($and thus being in a crash$)?$ How does this probability vary with $?$ Provide some

intuition for why this is the case.

$4.$ How would the equilibria of the game change if $>1?$