Game 9: Dividing Grades Description Adam, Bob, Carl, and Dave copied an assignment off each other. The professor caught them and was rather unimpressed. He informs the four students that the assignment was done correctly and that it deserves 100%. But there's a catch: since there was only effectively a single unique a55ignrnent submitted [the others were copies]. the four students have to divide the 100 points in whatever wag,r they see t. The one condition is that every student must receive a nonnegative integer number of points. For example, the students could choose the split [2 5, 25, 25, 25] or [i], I], I], 100], but not [25.5, 25, 25, 24.5]. The students agree on the following process for dividing the grade. Adam gets to propose a division of the 100 points. Then all four students [including the proposer] vote in favour or against the proposed division. If at least half of the votes are in favour; that is how the points are divided. If fewer than half of the votes are in favour; Adam gets kicked out of the group [receiving 0] and Bob gets to propose a new division of the 100 points among the remaining three students. That is; at every stage, the student whose name is first alphabetically among the remaining students makes a proposal. If it is accepted {i.e. half or more of the remaining individuals including the proposer are in favour], that is how the points are divided. If it is rejected [fewer than halfof remaining individuals vote in favour], the proposing individual is kicked out of the group receiving 0, and the next individual proposes a split among the remaining students. The game ends when a proposal is accepted by half or more of the remaining students, or when all the students have been kicked out