Question

Suppose two players are sitting at a table and in Round 1, a benevolent God puts one

dollar on the table. Player 1 gets to decide whether to leave with the dollar or whether they
should continue on to the next round. In Round 2. God puts another dollar on the table and
gives Player 2 the chance to leave with two dollars or whether to continue to the next
round. In Round 3. God puts two more dollars on the table, and it is Player 1's choice
whether to leave with three dollars (and Player 2 with one dollar) or to continue. Finally in
Round 4. God puts two more dollars on the table and Player 2 decides whether to leave
with four dollars or to continue. If Player 2 chooses continue in Round 4, then God adds
another dollar and the final payoffs are: Player 1 receives four dollars and Player 2 receives 3 Dollars.

The game is outlined as follows. Once a player chooses to leave the game, the game ends (Stops.) Therefore, the choice for each player in each round is S or C. S means leave the game (stop) and C means continue to the next round.
CONSIDER THE FOLLOWING STATEMENTS:
I. There is no unique Nash equilibrium of this game.
II. In equilibrium, the deadweight loss is $6
Ill. Player 2 has a follower advantage in this game.
IV. The only equilibrium outcome is for the players to receive (4,3).


WHICH OF THESE STATEMENTS ARE TRUE:
A. 1 only
B. Il only
C. Ill. only
D. only
E. ll. and Ill.
F. ll. and IV.
G. I, Ill, and IV.
H. All of them.
I. None of them

Answer 1

The true statements about the given game are about the deadweight loss, the follower advantage, and the equilibrium outcome.

Step-by-step explanation:

The statements that are true about the given game are:

1. Statement II. In equilibrium, the deadweight loss is $6
2. Statement III. Player 2 has a follower advantage in this game.
3. Statement IV. The only equilibrium outcome is for the players to receive (4,3).

Statement I is false because there is a unique Nash equilibrium in this game. The Nash equilibrium is for Player 1 to continue in Round 1 and for Player 2 to continue in Round 2 and Round 4.

Therefore, the correct answer is G. I, III, and IV.