Part a: ['10 pts] Consider the following dynamic scenario between George, Barack, and Donald: Initially there are 2 one dollar bills on the table. George rst comes to the table and decides how much money to take from the table. George can decide either to take no money, take one dollar, or take 2 dollars from the table. If there is no money remaining on the table, then the game ends. Otherwise, Barack comes to the table second. Barack observes the number of dollars remaining on the table and decides either to take no money or a whole number of dollars from the table (if there are two dollars remaining, Barack can either take U,1,or 2 dollars from the table). Again if there is no money remaining on the table, the game ends. Otherwise, Donald comes to the table last. Donald observes hov.r many dollars are remaining on the table but does not know exactly who took how much money. Given this information, Donald decides how many of the remaining dollar bills to take [again what Donald takes must be a whole number or zero}. After this decision the game ends. The payoffs are as follows: each player obtains a utility equal to the amount of money that he took minus a cost of 10 that he incurs if and only if he was the only one to take any money. For example, if George was the only one to take any money and George took 2 dollars, George would get a utility 2 10 = 3. On the other hand, if George and Barack both took one dollar while Donald took none, then George and Barack would both get 1 utility while Donald would get zero utility. Write down the extensive form of this game. How many subgames does this extensive form game have? How many strategies does Donald have in this game? Part ll: [15' ptsf Consider the following normal form game between player 1 (row player) and player 2 [column player}. Let ((o, b, c), (d, e, f)) represent the mixed strategy prole where player 1 chooses A with prob- ability :1, B with probability in, and C with probability c; player 2 chooses D with probability d, E with probability 6, and F with probability f. Consider the following strategy proles: 1. [(2,1'3, 1,33, [1), (1/2, 1/2, 0)), 2. [0,3/4,1;4),(1/2,0,1/2)). Which of the above strategy proles (if any) are Nash equilibria? Justify your answer for each of the strategyr proles