THE PIRATE GAME 1. Suppose there are 100 gold coins and 5 pirates. The 5 pirates put 5 numbers (1,2,3,4,5) in a hat and randomly pick out a number. This process determines the sequence in which the pirates proceed in the game. The pirate who picked #1 gets to decide how many coins to allocate to himself and to every other pirate. Then all the pirates vote on this allocation. If AT LEAST HALF of the pirates (including the allocator) consider this a suitable allocation, then the game ends. However, if the allocation is not approved by at least half of the pirates, the pirate #1 is killed and the game starts over with the initial order (ie with 4 pirates and #2 as the allocator, #3 as the next guy, #4 as two from the beginning, etc). This process (i.e. vote and either end the game or kill the allocator) continues until the game ends or only 2 pirates are left. Assuming that all pirates are strictly rational, how will the coins be allocated?