Game Theory - Econ 3M03 Fall 2014
Quiz 4
Version 1
1. There are two piles of money--one labelled "for Player 1" and one labelled "for Player
2". At the beginning of the game, each pile has 2 dollars in it. The players take turns
deciding to either continue the game or end it. Each player (beginning with player 1) will
get three such turns. If a player decides to end the game, then each player receives the
pile of money that is for that player (and the game ends). Whenever a player decides to
continue the game, then 1 dollar is taken from the pile for that player and moved to the
pile for the other player where it magically becomes 2 dollars and then it is the other
player's turn to decide. (So, for example, in the first turn of the game, if player 1 decides
to continue, his pile is reduced by 1 dollar to become a pile with only 1 dollar, but player
2's pile increases by 2 dollars to become a pile with 4 dollars.) If they each choose all
three times to continue the game, then it still ends at that point and each player gets their
pile. (So it is equivalent to player 1 having a 4th "turn" in which his only choice is to end
the game.)
What is(are) the subgame-perfect Nash equilibrium(s) of this game?
Version 2
1. There are two piles of money--one labelled "for Player 1" and one labelled "for Player
2". At the beginning of the game, each pile has 3 dollars in it. The players take turns
deciding to either continue the game or end it. Each player (beginning with player 1) will
get three such turns. If a player decides to end the game, then each player receives the
pile of money that is for that player (and the game ends). Whenever a player decides to
continue the game, then 2 dollars are taken from the pile for that player and moved to the
pile for the other player where it magically becomes 3 dollars and then it is the other
player's turn to decide. (So, for example, in the first turn of the game, if player 1 decides
to continue, his pile is reduced by 2 dollars to become a pile with only 1 dollar, but player
2's pile increases by 3 dollars to become a pile with 6 dollars.) If they each choose all
three times to continue the game, then it still ends at that point and each player gets their
pile. (So it is equivalent to player 1 having a 4th "turn" in which his only choice is to end
the game.)
What is(are) the subgame-perfect Nash equilibrium(s) of this game?
Version 3
1. There are two piles of money--one labelled "for Player 1" and one labelled "for Player
2". At the beginning of the game, each pile has 1 dollar in it. The players take turns
deciding to either continue the game or end it. Each player (beginning with player 1) will
get three such turns. If a player decides to end the game, then each player receives the
pile of money that is for that player (and the game ends). Whenever a player decides to
continue the game, then 1 dollar is taken from the pile for that player and moved to the
pile for the other player where it magically becomes 3 dollars and then it is the other
player's turn to decide. (So, for example, in the first turn of the game, if player 1 decides
to continue, his pile is reduced by 1 dollar to become a pile with zero dollars, but player
2's pile increases by 3 dollars to become a pile with 4 dollars.) If they each choose all
three times to continue the game, then it still ends at that point and each player gets their
pile. (So it is equivalent to player 1 having a 4th "turn" in which his only choice is to end
the game.)
What is(are) the subgame-perfect Nash equilibrium(s) of this game?
Version 4
1. There are two piles of money--one labelled "for Player 1" and one labelled "for Player
2". At the beginning of the game, each pile has 4 dollars in it. The players take turns
deciding to either continue the game or end it. Each player (beginning with player 1) will
get three such turns. If a player decides to end the game, then each player receives the
pile of money that is for that player (and the game ends). Whenever a player decides to
continue the game, then 1 dollar is taken from the pile for that player and moved to the
pile for the other player where it magically becomes 2 dollars and then it is the other
player's turn to decide. (So, for example, in the first turn of the game, if player 1 decides
to continue, his pile is reduced by 1 dollar to become a pile with only 3 dollars, but player
2's pile increases by 2 dollars to become a pile with 6 dollars.) If they each choose all
three times to continue the game, then it still ends at that point and each player gets their
pile. (So it is equivalent to player 1 having a 4th "turn" in which his only choice is to end
the game.)
What is(are) the subgame-perfect Nash equilibrium(s) of this game?