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Greedy Pirates and Backward Induction (Game Theory)
Three pirates stand atop the bow of their ship. Their names are Samuel, Morgan and Henry. Each is in higher command from the next. They are preparing to split the bounty from their latest siege of 100 coins.
An ancient tradition dictates how the pirates will divvy their keeps. As per the code, the strongest (Samuel) reminds them of the rules.
The sequence of rules are as follows:
- Samuel (1) will propose a split of the treasure
- The crew votes on the proposal
- If Samuel (1) is outvoted, he is forced to walk the plank
- Morgan (2) now proposes a split with Henry (3)
- If there is a tie, Morgan (2) is allowed the final vote on the subsequent offer
After some contemplation, Samuel offers his proposed split: 40% goes to Samuel, then 30% to Morgan and Henry..
“A fair offer” says Samuel, “without my leadership… our raid would have failed”
Morgan aggressively declines. Yet Henry is torn. “If I refuse, Sam walks… but Morgan and I may split 50–50”, he thinks to himself.
A few moments later, Samuel is killed. With a wry smile on his face, Morgan takes all the treasure…
