How to divide the stolen gold bars? Five robbers,

How to divide the stolen gold bars? Five robbers, Adam, Bob, Chuck, Dave and Eric (ordered by the level of experience, with Eric being the most experienced), just robbed a bank and stole 100 gold bars. Now they are hiding in a cave, where there are hungry wolves roaming outside. The key problem they need to resolve is how to split the gold bars among themselves. After a long grueling debate, they settle on the following process for determining how to split the fortune: starting from Eric (and follow the decreasing order of experience), each time one person proposes a way to split the gold bars among all (surviving) robbers. For example, Eric could propose to give himself 60 bars, and give each of the rest 10 bar each. If at least half (yes the one proposing the plan is counted) of the remaining guys agree to the proposed way of splitting the gold bars, that is the final way of splitting the fortune and the process stops; otherwise, the one who just proposed the splitting plan must leave the cave (and will surely be eaten by the wolves) and then the process continues. Now imagine you are Eric. Tell me what you are going to propose the way of splitting the fortune. You need to justify your answer. Note: you can assume each person is selfish and logical: each wants to be alive and at the same time he wants the maximum amount of gold bars. In case you still have energy left after working on this homework, you can think about the following questions: what if there are k = 6, 7, … robbers? is it always better to be the first to propose a splitting method? If not, how many robbers will there be in that case? You don’t need to answer these and no solutions will be given for these questions. But if you answer these correctly, you get 5% extra credits. Show transcribed image text How to divide the stolen gold bars? Five robbers, Adam, Bob, Chuck, Dave and Eric (ordered by the level of experience, with Eric being the most experienced), just robbed a bank and stole 100 gold bars. Now they are hiding in a cave, where there are hungry wolves roaming outside. The key problem they need to resolve is how to split the gold bars among themselves. After a long grueling debate, they settle on the following process for determining how to split the fortune: starting from Eric (and follow the decreasing order of experience), each time one person proposes a way to split the gold bars among all (surviving) robbers. For example, Eric could propose to give himself 60 bars, and give each of the rest 10 bar each. If at least half (yes the one proposing the plan is counted) of the remaining guys agree to the proposed way of splitting the gold bars, that is the final way of splitting the fortune and the process stops; otherwise, the one who just proposed the splitting plan must leave the cave (and will surely be eaten by the wolves) and then the process continues. Now imagine you are Eric. Tell me what you are going to propose the way of splitting the fortune. You need to justify your answer. Note: you can assume each person is selfish and logical: each wants to be alive and at the same time he wants the maximum amount of gold bars. In case you still have energy left after working on this homework, you can think about the following questions: what if there are k = 6, 7, … robbers? is it always better to be the first to propose a splitting method? If not, how many robbers will there be in that case? You don’t need to answer these and no solutions will be given for these questions. But if you answer these correctly, you get 5% extra credits.