New Rule Description: Multiple Lives

Given the game we decided to make some experiments adding some new rules. The first one we thought regards adding multiple lives to the pirates. This idea turns out to be very interesting because it gives a new dynamic in the decision and reasoning process: in fact, in case a pirate proposal is rejected, the next pirate will have the turn to make his proposal, but the previous pirate, instead of dying, still has a right to vote. Even if from an intuitive point of view the result may be different, if we reason on case based, or we look at the graph, we can see that the outcome is the same. By giving multiple lives, it's true that we add many more worlds, but when we reason, we find that since we have to consider the possible endings from the last one (the case where there are only two pirates alive), all we are doing is adding steps to the backward solution, but the last (so the first proposal of the first pirate) is still based on the possible future ones. A pirate's proposal always follows the same “rule”: give money to the pirates that wouldn't receive any in the next (future) solution; in this way we can secure a successful vote from them. The graph interprets the whole process step-by-step..

It is important to distinguish two main "branches": one represents the "Multiple Lives" case, and the other one indicates the "Single life" case. They explain the reasoning steps in both situations. It's important to notice the red line connection: in fact, it represents a close loop. When the pirates have more than one life left, the model is closed into the loop: they can keep voting, rejecting other's proposals, and still be alive. As soon as the pirates have only one life left, we pass to the "SingleLife" branch. Once we pass to this "branch", it's easy to see how it is connected to the normal game, with the default rule. In conclusion, adding the multiple lives to pirates doesn't really change the main rules of the game (especially the "Survival" rule) as expected; but instead, this new rule adds loops in "Multiple Lives" branch, as many times as the lives of the pirates.