# Game theory

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Problem 1

1. Suppose you and one of your two roommates have just finished

cleaning your dorm suite and found 13 quarters which you put on a

table in the middle of the room. The third roommate who did none of

the cleaning comes in from an afternoon of fun and relaxation and

proposes that you divide the coins up the following way: The two who

cleaned and collected the quarters will take turns after flipping a coin

to see who goes first. At each turn the player has a choice to take 1 or

2 quarters. If the player takes 1 coin, then the next player gets a turn. If

the player takes 2 coins, then the game ends and the third roommate

gets the rest of the money on the table.

a. The roommate who helped you clean says, "Okay that sounds fair.

Let's play." Do you agree? Support your answer by determining

what the equilibrium outcome of the game will be. (i.e., indicate

how much money each roommate will get and why). State the

assumptions you make. (Hint: what would you do if it was your

turn and there were two coins left?)

b. If you and the roommate who helped you clean could write a

binding contract describing how each would play the game, what

might the contract say? How would the outcome of the game

played according to the contract differ from the game as played in

part a.?

c. The game in part a. is a repeated game in the sense that several

turns are possible. In a repeated game there is an opportunity to

build or erode trust. Can you image getting an outcome similar to

that in b without a contract? Explain.

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##### Solution Summary

This is a problem dealing with game theory and personal choices. The repeated games that erode trust are given.

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Problem 1

1. Suppose you and one of your two roommates have just finished cleaning your dorm suite and found 13 quarters which you put on a table in the middle of the room. The third roommate who did none of the cleaning comes in from an afternoon of fun and relaxation and proposes that you divide the coins up the following way: The two who cleaned and collected the quarters will take turns after flipping a coin to see who goes first. At each turn the player has a choice to take 1 or 2 quarters. If the player takes 1 coin, then the next player gets a turn. If the player takes 2 coins, then the game ends and the third roommate gets the rest of the money on the table.

a. The roommate who helped you clean says, "Okay that sounds fair. Let's play." Do you agree? Support your answer by determining what the equilibrium outcome of the game will be. (i.e., indicate how much money each roommate will get and why). State the

assumptions you make. (Hint: what ...

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