Pirate game
The pirate game is a simple math game . It illustrates how surprising results can be when the assumptions of the Homo oeconomicus model on human behavior hold up. It is a multiplayer version of the ultimatum game .
game
There are five rationally acting piratesA, B, C, D and E that find 100 gold coins. You now have to decide how to divide this up among yourself. There is a strict hierarchy of age among pirates: A is higher in rank than B, who is higher than C, who is higher than D, who is in turn higher than E. The distribution rules in the pirate world are as follows: The highest ranking pirate makes a proposal for the distribution of the coins, then the pirates vote whether they accept this distribution proposal. The proposer can vote and has the casting vote in the event of a tie. If the proposal is accepted, the division will be as proposed; otherwise the proposer is thrown overboard and the highest-ranking pirate remaining is given the opportunity to propose a division - the game starts over with a reduced number of players.
The pirates decide based on three criteria: First of all, every pirate wants to survive. Second, every pirate wants to maximize the number of gold coins they receive. And third, every pirate would like to throw the others overboard if the other criteria remain the same.
Result
It could be intuitively assumed that pirate A is forced to give himself little to nothing, as he may fear being overruled with his proposal so that the loot can be divided among a then smaller group of pirates. Nevertheless, the theoretical result looks very different.
This becomes obvious if we approach the solution in reverse: If all but D and E are already overboard, D can propose 100 for himself and 0 for E. He has the casting vote and so the distribution is accepted.
When there are three pirates left (C, D and E), C predicts that D will offer E 0 in the next round; therefore, in this round, C must offer E (at least) 1 in order to receive E's vote and enforce his distribution proposal. So the distribution with three remaining pirates is C: 99, D: 0 and E: 1.
If there are B, C, D, and E left, B anticipates all of this in making his decision. In order not to be thrown overboard, he can simply offer D 1. Since he has the casting vote, D's support is sufficient. So he suggests B: 99, C: 0, D: 1 and E: 0. One could also consider proposing B: 99, C: 0, D: 0, and E: 1, since E is sure not to get any more if he throws B overboard. However, since each of the pirates is happy to throw one of the others into the sea, E would prefer to throw B overboard and get the same amount of gold from C.
Assuming A knows about all this, he can count on the support of C and E for the following division, which is also the final solution:
- A: 98 coins
- B: 0 coins
- C: 1 coin
- D: 0 coins
- E: 1 coin
In contrast, the division A: 98, B: 0, C: 0, D: 1, E: 1 is just as impossible as other variations, since D prefers to throw A overboard and receive the same amount of gold from B.
extension
The game can easily be expanded to include up to 200 pirates without changing the outcome. If you expand the number of pirates to over 200 pirates and leave the amount of money unchanged, the pattern changes. Ian Stewart expanded the game in Scientific American (May 1999 edition) to include any number of pirates and came to other interesting results: from 201 pirates, only pirates 1 to 200 receive one gold coin each, the pirates' request from 201 is then only survival. However, the analysis shows that only those pirates survive whose atomic number is of the form "200 plus a power of two".
See also
Individual evidence
- ↑ a b c Ian Stewart : A Puzzle for Pirates (PDF; 1.8 MB) pp. 98–99. May 1999. Retrieved December 2, 2012.