Consider the following dynamic scenario between George, Barack, and Donald: Initially there are 2…

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

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?

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