Your Name: ____________________________
Final Exam: 18 Dec 2003
You have 120 minutes to take this exam.
There are a total of 100 points possible, plus
three extra-credit questions (1f, 1g, 4g) worth a total of 20 points. Please make sure to
pace yourself, so that you answer all questions, even incompletely.
I do give partial
credit for incomplete work, but I give zero credit for blank pages.
In order to get partial
credit in case you make an error, you will want to explain carefully what you are doing.
In the game show The Weakest Link, players take turns answering questions; each
right answer adds to a pot of money for the group.
After each round of questions, the
players vote to remove one of their group from the game.
A player who leaves the
game receives zero prize money.
When there are only two players left, there is one
round of questions in which the two players again add to the pot with correct answers.
Following this round, instead of a vote to determine the winner, the winner is
determined by a final round of questions; whoever answers more questions correctly
is the winner of the pot of money.
An interesting question is whether it makes sense
strategically for players to want to vote off the player who answers the fewest
questions correctly, also known as the “weakest link.”
For a simplified analysis of equilibrium behavior in this game, let’s consider what
happens starting from the point where the final three players are choosing which one
of them will be “voted off” the game.
Suppose that at this point there is a pot of
$1000 already accumulated.
Suppose also that the three players have three different
abilities in answering questions: player A has an ability of 0.9, Player B has an ability
of 0.5, and Player C has an ability of 0.3.
After the voting, each remaining player
will manage to add to the pot an amount equal to $500 times her ability.
example, if Players A and B remain, then the final pot will equal $1000 + 0.9($500) +
0.5($500), for a total of $1700.)
After the final amount of the pot has been
determined, suppose that in the final round the remaining player with the higher
ability will win the entire pot, and the player with the lower ability will lose (earn a
payoff of zero).
In the voting game, each player may vote for one of the other two players.
decided by a plurality rule.
In case of a tie, the highest-ability player (the “strongest
link”) gets to break the tie in her own favor.