Pirate game
The Pirate game is a simple mathematical game. It illustrates how surprising results may be, if the assumptions of the homo economicus model of human behavior withstand. It is a multi-player version of the ultimatum game.
Game
Given are five acting rationally Pirate A, B, C, D and E, which are 100 gold coins. You must now decide how to share this with each other. Among the pirates there is a strict hierarchy according to age: A is senior to B, which is higher in rank than C, which is higher in rank than D, which in turn is higher in rank than E. The distribution rules in the pirate world look like this: The most senior pirate makes a proposal to divide the coins, then the pirates agree on whether they accept this proposal distribution. The proposer may also vote and shall have the casting vote in case of a tie. If adopted, the division takes place as proposed; Otherwise, the proposer is thrown overboard and the highest maintained pirate will have the opportunity to propose a division - the game starts over.
The pirates decide on the basis of three criteria: First of all, each pirate wants to survive. Second, everyone wants to pirate the number of gold coins he receives maximize. And third, each pirate would love to throw the other overboard when the other criteria remain the same otherwise.
Result
It could be assumed intuitively that Pirate A is forced themselves allot little to nothing because he could fear being outvoted with his proposal so that the prey can be divided among a smaller group of pirates then. Nevertheless, the theoretical result looks far different.
This becomes obvious when we approach reversed the solution: If all except D and E already overboard, D may propose for itself 100 and 0 for e. He has the casting vote, and so the distribution is assumed.
If three pirates are left (C, D and E), white C, D that will offer in the next round E 0; therefore must (at least) one offer to the voice of e to obtain and enforce its proposed distribution of C in this round e. Accordingly, the distribution is with three remaining pirates C: 99, D: 0 E: 1
If B, C, D and E are left white B in its decision all this already. To it can not be thrown overboard D just 1 offer. Since he has the casting vote is the support of D sufficient. Consequently, he proposes B: 99, C: 0, D: 1 and E: 0 ago. You might also consider B: 99, C: 0, D: 0, and E: to propose one, since E is not more to get sure that if he throws B overboard. However, since each of throwing a pirate like the other into the sea, I would prefer B to throw overboard and get the same amount of gold C.
Suppose A is aware of all this, he can expect the following distribution with the support of C and E, which also represents the final solution:
- A: 98 coins
- B: 0 Coins
- C: 1 coin
- D: 0 Coins
- E: 1 coin
Also A: 98, B: 0, C 0, D 1, E 1 or any other variations are possible, since D A rather raises overboard is replaced by the same amount of gold B.
Extension
The game can easily be extended to up to 200 pirates, without changing the result. However, it expands the number of pirates over 200 pirates and leaves the money supply unchanged, changed the pattern. Ian Stewart advanced the game in Scientific American ( May 1999 edition ) on any number of pirates and were further interesting results.