1matching pennies (35 points) a) (7 points) the normal form of the game was given in the lecture. draw the extensive form of this b) (7 points) in the lecture, this was presented as a siultaneous ove game (both players lipped at the matching pennies in a game of matching pennies, player 1 and player 2 both flip a penny in the air at the same time. if the pennies both land heads-up or both land tails-up then we say the pennies match and player 1 gets to keep both pennies. if the pennies "mismatch with one being heads-up and the other tails-up, then player 2 gets to keep both pennies game same time). what would be the difference), if any, if it were n seqaential move game (the second player hips after the first player's bip is finished)? c) (7 points) now assume that instead of flipping a penny randomly and letting nature determine whether player 2 ails it lands heads or tails, each player gets to write down either "hads or "tails" on a piece of paper the papers are revealod simultanesly. what would be the diffcrences), if any, compared to the situntion where nature determines the outoome? d) (7 points) assume that rather than ipping a coin, players are writing down "heads" or tails and it is a sequential game. draw the game tree with payouts. e) (7 points) in part d, is there an advantage to being either the first moveτ ar second mower? why or matching pennies is a game of imperfect information because each player is unsure of what his or her move will be. therefore the other player cannot knaw or be able to choosel which move to make at every nade in the game tree. why not?