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A group of N pirates has come by a chest containing 200 gold coins. Their rules require that the coins be distributed by the following approach. The pirates are ranked from fiercest to meekest and all pirates know the ranking. The fiercest must propose a division, which is put to majority vote with the fiercest winning ties. If the proposal wins, it is implemented. If not, the fiercest is fed to the sharks and the responsibility falls to the (newly promoted) fiercest. The pirates are selfish and quite rational, with the following priorities:

1. Stay alive
2. Get as much gold as possible, as long as 1 is satisfied
3. If 1 is satisfied and two options are equivalent in terms of gold, feed somebody to the sharks by preference.

Depending on N, what happens? To be complete, your answer should deal with large values of N. Source: I first saw it in a Martin Gardner column.

A group of N pirates has come by a chest containing 200 gold coins. Their rules require that the coins be distributed by the following approach. The pirates are ranked from fiercest to meekest and all pirates know the ranking. The fiercest must propose a division, which is put to majority vote with the fiercest voting and winning ties. If the proposal wins, it is implemented. If not, the fiercest is fed to the sharks and the responsibility falls to the (newly promoted) fiercest. The pirates are selfish and quite rational, with the following priorities:

1. Stay alive
2. Get as much gold as possible, as long as 1 is satisfied
3. If 1 is satisfied and two options are equivalent in terms of gold, feed somebody to the sharks by preference.

Depending on N, what happens? To be complete, your answer should deal with large values of N. Source: I first saw it in a Martin Gardner column.