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    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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    https://brainmass.com/math/discrete-math/game-theory-and-personal-choices-3269

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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 ...

    Solution Summary

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

    $2.19

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