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 first 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 0,1,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 how 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 = -8. 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
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?