Game Development Reference
In-Depth Information
In the Pirate Game, we have a number of
rational
pirates (for this example we
will use five). Despite my desire to come up with really cool pirate names, we will
refer to them as A, B, C, D, and E. The alphabetical monikers actually help us with
the next issue, that 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.
As a group, the five pirates find 100 gold coins and are trying to decide how to
distribute them. In the pirate's world the rules of distribution are as follows.
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.
The proposer has the
casting
vote in the event of a tie.
If the proposed allocation is approved by vote, that proposal goes into effect.
If the vote fails, the proposer is thrown overboard from the pirate ship and dies.
The next most senior pirate makes a new proposal to begin the process again.
Pirates base their decisions on four factors. Each pirate:
1. Is entirely rational.
2. Wants to survive.
3. Wants to maximize the amount of gold coins he receives.
4. Would prefer to throw another overboard, if all other results would other-
wise be equal.
At first glance, it would seem that pirate A, being outnumbered by his peers,
might have to minimize his own allocation to avoid getting kicked off. After all, if
the other four pirates think he is taking too much, they would stand to benefit by
declining his proposal and sending him down the stereotypical plank. At that point,
the total would only be divided among the four of them, rather than five. This,
however, is not the solution—and is surprisingly divergent from his optimal approach.
Iterating Perfectly Rational Decisions
The pure strategy solution becomes more apparent if we work backward. To do so,
let's assume that somehow we managed to get down to the final two pirates, D and
E. Knowing that, as senior pirate, he has the deciding vote over E, D proposes 100
for himself and zero for the hapless E. E can't do anything about it, so this would
be the final result when it is just the two of them.
