Consider a game where two players take turns deciding whether or not to take a p

ID: 1227576 • Letter: C

Question

Consider a game where two players take turns deciding whether or not to take a pile of money. At the start of the game, there are two piles of money, one "large" pile with 5 dollars and one "small" pile with 1 dollar. Player 1 gets to choose whether to take the large pile, or leave both piles alone.

- If player 1 takes the large pile, he receives 5 dollars as his payoff, and player 2 receives the small pile, 1 dollar, as his payoff, and the game ends.

- If player 1 leaves both piles alone, both the large and the small piles double (10 dollars, and 2 dollars, respectively)

- Player 2 then decides whether to take the large pile of leave both piles alone.

- Every time a player leaves both piles alone, both piles double in size.

- Players take turns deciding whether to take the large pile or leave the piles alone until each player has had three oppourtunites to take the large pile (six rounds total).

- If, at the end of the game, neither play has taken the large pile, player 1 is awarded the large pile (which will contain 320 dollars at this point) and player 2 is awarded the small pile (which will contain 64 dollars).

1. Label the best response at every stage of the game. What will the outcome of this game be?

Explanation / Answer

For the extensive form of game depiction below:

LP= Large Pile

SP=Small Pile

NC=No choice

At each stage of decision making the player does better with Large Pile than the Small Pile and the best response at each stage is given in yellow in the diagram below.

However, both know that if they do not choose at any stage at the end Player 1 will get 320 while Player 2 will get 64 which is better than any payoff at any other point. So on mutaul consent they should go for not chossing at any stage and eraning 320,64 at the end this would be the outcome of the game.

PLAYER 1 11

(5,1)

(1,5)

(0,0)

PLAYER 2

(2,10)

(10,2)

(0,0)

PLAYER 2

(8,40)

(40,8)

(0,0)

PLAYER 1

(80,16)

(16,80)

(0,0)

PLAYER 2

(32,160)

(160,32

(320,64)

PLAYER 1

(20,4)

(4,20)

(0,0)

PLAYER 1 11

Navigate

Consider a game where each player picks a number from 0 to 60. The guess that is

Consider a game where two players take turns deciding whether or not to take a p

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.

Consider a game where two players take turns deciding whether or not to take a p

Question

Explanation / Answer

Related Questions

Navigate