Pirate game

Pirate game

The pirate game is a simple mathematical game. It illustrates how, if assumptions conforming to a homo economicus model of human behaviour hold, outcomes may be surprising. It is a multi-player version of the ultimatum game.

The Game

There are five rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them.

The Pirates have a strict order of seniority: A is superior to B, who is superior to C, who is superior to D, who is superior to E.

The Pirate world's rules of distribution are thus: that the most senior pirate should propose a distribution of coins. The pirates should then vote on whether to accept this distribution; the proposer is able to vote, and has the casting vote in the event of a tie. If the proposed allocation is approved by vote, it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again.

Pirates base their decisions on three factors. First of all, each pirate wants to survive. Secondly, each pirate wants to maximize the amount of gold coins he receives. Thirdly, each pirate would prefer to throw another overboard, if all other results would otherwise be equal.

The Result

It might be expected intuitively that Pirate A will have to allocate little if any to himself for fear of being voted off so that there are fewer pirates to share between. However, this is as far from the theoretical result as is possible.

This is apparent if we work backwards: if all except D and E have been thrown overboard, D proposes 100 for himself and 0 for E. He has the casting vote, and so this is the allocation.

If there are three left (C, D and E) C knows that D will offer E 0 in the next round; therefore, C has to offer E 1 coin in this round to make E vote with him, and get his allocation through. Therefore, when only three are left the allocation is C:99, D:0, E:1.

If B, C, D and E remain, B knows this when he makes his decision. To avoid being thrown overboard, he can simply offer 1 to D. Because he has the casting vote, the support only by D is sufficient. Thus he proposes B:99, C:0, D:1, E:0. One might consider proposing B:99, C:0, D:0, E:1, as E knows he won't get more, if any, if he throws B overboard. But, as each pirate is eager to throw each other overboard, E would prefer to kill B, to get the same amount of gold from C.

Assuming A knows all these things, he can count on C and E's support for the following allocation, which is 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 other variants are not good enough, as D would rather throw A overboard to get the same amount of gold from B.

Extension

The game can easily be extended to up to 200 pirates (or further if you increase the amount of gold). Ian Stewart extended it to an arbitrary number of pirates in the May 1999 edition of Scientific American, with further interesting results.Citation |url=http://euclid.trentu.ca/math/bz/pirates_gold.pdf| last = Stewart | first = Ian | author-link = Ian Stewart (mathematician) | year = 1999 | date = 1999-05 | title = A Puzzle for Pirates | periodical = Scientific American | publication-date = 1999-05 | pages = 98–99 ]

References

ee also

* Creative problem solving
* Lateral thinking


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Pirate game — Aus Howard Pyle s Book of Pirates Das Pirate game ist ein einfaches mathematisches Spiel. Es illustriert wie überraschend Ergebnisse sein können, wenn die Annahmen des Homo oeconomicus Modells zum menschlichen Verhalten standhalten. Es ist eine… …   Deutsch Wikipedia

  • Pirate Baby's Cabana Battle Street Fight 2006 — is a 12 minute, black and white animated movie by Paul Laurence Robertson, featuring music by Cornel Wilczek, also known as Qua. It depicts a fictional side scroller video game, heavily influenced and inspired by anime, cult 1980s platform games… …   Wikipedia

  • pirate — pi‧rate [ˈpaɪərət ǁ ˈpaɪrət] noun [countable] LAW 1. a person or organization that dishonestly copies and sells films, tapes etc for which the copyright (= legal ownership) belongs to others: • Manufacturers fear that the city may emerge as a new …   Financial and business terms

  • Pirate Master — infobox television show name = Pirate Master format = Reality, Game Show winner = Ben Fagan runtime = 60 minutes location = Dominica creator = Mark Burnett starring = Cameron Daddo (host) country = USA network = CBS, CBS.com first aired = May 31… …   Wikipedia

  • Pirate Ship Higemaru — Infobox VG title=Pirate Ship Higemaru developer = Capcom publisher = Capcom designer = Tokuro Fujiwara released=September 1984 genre =Action/Puzzle modes =Single player, 2 player Alternating platforms=Arcade arcade system= Capcom Z80 basedPirate… …   Wikipedia

  • Pirate (disambiguation) — NOTOC Pirate can refer to:Criminal acts of piracy* Piracy, specifically maritime piracy * Aircraft hijacking, commonly known as air piracy * Biopiracy * Copyright infringement * Misappropriation of traditional knowledge * Oyster pirate * Patent… …   Wikipedia

  • Pirate television — A pirate television station is a broadcast TV station that operates without official or government licensing.Like its counterpart pirate radio, the term pirate TV lacks a specific universal interpretation. It implies a form of broadcasting that… …   Wikipedia

  • Pirate code — A pirate code was a code of conduct invented for governing pirates, and first introduced by the Portuguese buccaneer, Bartolomeu Português. Generally each pirate crew had its own code or articles, which provided rules for discipline, division of… …   Wikipedia

  • Pirate Islands — Infobox Television show name = Pirate Islands caption = Pirate Islands Title Screen genre = Sci Fi Children s creator = Jonathan M. Shiff Greg Millin director = Richard Jasek starring = Brooke Harman Eliza Taylor Cotter Nicholas Donaldson Oliver… …   Wikipedia

  • Pirate and Traveler game — The board game Pirate and Traveler was first marketed by Milton Bradley in 1911. Revised editions were published in 1936, 1953, 1956, 1960, and 1970. The game is no longer in production. Details of the game board, travel cards, spinner, box art,… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”