Problem $2We$ consider the following game. There are two players, Alice and Bob. Bob

can $beof$ two types, ${}_1$ and ${}_2.He$ knows his type but Alice does not.

The probability that Bob $isof$ type ${}_{1}isp=0\mathrm{.}6,$ and Alice knows that.

The payoffs are given $in$ Table $2.$

A Bayesian$-$Nash equilibrium $is$ called a pooling equilibrium $if$ the informed player,

Bob, plays the same action regardless $of$ his type. $Is$ there such $an$ equilibrium? $If$ yes,

give the equilibrium strategy profile. Justify your answers.

Bob $isof$ type ${}_1,$ Bob $isof$ type ${}_2$

Table $2$: A two player game

A Bayesian$-$Nash equilibrium $is$ called a separating equilibrium $if$ the informed player,

Bob, plays a different action depending $on$ his type. $Is$ there such $an$ equilibrium? $If$

yes, give the equilibrium strategy profile. Justify your answers.