Exercise $6\mathrm{.}2.$ The two$-$person game shown in Table $6\mathrm{.}9$ has a unique

Nash equilibrium $($see Moulin and Vial, $1978)$ in which each player's

expected payoff is $3.$

a$.$ Show that this game has correlated equilibria in which both players

get expected payoffs strictly larger than $4.$

b$.$ Find the correlated equilibrium that maximizes' the expected payoff

for player $1.$