nature $$ and $.$ Each of the states is associated with a payoff matrix as

follows:

$$

$$

There is a common prior belief that the state $$ is more likely with a

probability of $\frac{3}{5}.$ Before they play the game Alp gets to learn the true state of

nature but cannot directly share this information with Burcu. Instead, they

communicate only by electronic mail signals. Due to "technical difficulties"

there is a $0\mathrm{.}01$ probability that the message does not arrive at its destination.

At the risk of creating discord, the electronic mail network is set up to send a

confirmation automatically if any message is received, including not only the

confirmation of the initial message but a confirmation of the confirmation,

and so on$,$ yet, it is also commonly known that Alp's computer can

send at most $8$ messages, including the confirmations. If a message

does not arrive, then the communication stops. A message is sent from Alp's

computer only if the state of the nature is $,$ i$.$e$.,$ no message is sent if the

state of nature is $.$ At the end of the communication phase their computer

screen displays to each player the number of messages his$/$her computer has

sent. Each player chooses an action after observing the number on their

computer screen.

a$.$ Clearly model this game as a Bayesian Game.

b$.$ Can Alp and Burcu coordinate on playing $($A$,$A$)$ in $$ state of the world

and $(B,B)$ in $$ state of the world in a Bayesian Nash Equilibrium?

Why $/$ Why not?