Quorum Analysis for the \Pirate Game" Problem? Ilya Chernov1 and Evgeny Ivashko1;2 1 Institute of Applied Mathematical Research, Karelian Research Center of the Russian Academy of Sciences, Petrozavodsk, Russia 2 Petrozavodsk State University fchernov,
[email protected] http://mathem.krc.karelia.ru/ Abstract. The \Pirate game" is a popular mathematical puzzle, the problem aimed at demonstration of backward induction. It is also a shin- ing example of non-cooperative behaviour of rational agents in mathe- matical game theory. A linearly ordered crew votes for the captain's sharing offer. The captain needs the approval by a given fraction of the crew called quorum at the minimal cost. In this paper, we present the comprehensive quorum analysis on strategies and payoffs for the \Pirate game" problem, for any crew size and any quorum. Keywords: Pirate Game · Puzzle for Pirates · Quorum Analysis · Non- Cooperative Game Theory 1 Introduction and Related Work The \Pirate game" (also known as the \Puzzle for pirates") is a well-known widely-used mathematical puzzle, which often stirs up disputes3. The first ap- pearing of the problem in scientific literature seems to be in the book by E. Mou- lin [6] as an example; we found no earlier publications of this problem. The \Pirate game" is the following4: There are five rational pirates (in strict order of seniority A, B, C, D and E) who found 100 gold coins. They must decide how to distribute them. The pirate world's rules of distribution say that the most senior pirate first proposes a plan of distribution. The pirates, including the proposer, then vote on whether to accept this distribution.