To each of the following answer T or F and justify your answer:
a) Suppose we have a game G with an epistemic background such that (1) every player has beliefs consistent with knowledge, (2) every player is rational and (3) every player knows the type of every other player. Then such a game has a Nash Equilibrium.
b) Suppose we have a game G with an epistemic background such that (1) every player has beliefs consistent with knowledge, (2) every player is rational and (3) every player knows the type of every other player. Then such a game has a unique Nash Equilibrium.
c) Suppose we have a game G with an epistemic background such that (1) every player has beliefs consistent with knowledge, (2) every player is rational and (3) every player knows the type of every other player. Then any action profile is a Nash Equilibrium.