Suppose that nature selects normal$-$form game A or normal$-$form game B with probability $(1)/(2)$ each, and then Players $1$ and $2$ play the chosen normal$-$form game.

$($A$)$

$($B$)$

a$.$ Suppose that, when the players choose their actions, the players do not know which matrix has been chosen. That is$,$ they think that with probability $\backslash (1/2\backslash )$ the payoffs are as in matrix $\backslash ($ A $\backslash )$ and that with probability $\backslash (1/2\backslash )$ the payoffs are as in matrix B$.$ Write the normal$-$form of this Bayesian game. What strategy profile does IESDS predict?

b$.$ Now suppose that, before the players select their actions, Player $1$ observes nature's choice, but Player $2$ does not. Write the normal$-$form of this Bayesian game. What strategy profile does IESDS predict?

c$.$ Is the statement "A player benefits from having more information" true or false