The “Pirate game” is a popular mathematical puzzle, the problem aimed at demonstration of backward induction. It is also a shining example of non-cooperative behaviour of rational agents in mathematical 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.
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