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wedrifid comments on Nash Equilibria and Schelling Points - Less Wrong
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The actual equilibria can seem truly mind boggling at first glance. Consider this famous example:
There are 5 rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them.
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.
The pirate world's rules of distrubution are thus: that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. If the proposed allocation is approved by a majority or a tie vote, it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again.
Pirates base their decisions on three factors.
1) Each pirate wants to survive.
2) Given survival, each pirate wants to maximize the number of gold coins he receives.
3) Each pirate would prefer to throw another overboard, if all other results would otherwise be equal.
The pirates do not trust each other, and will neither make nor honor any promises between pirates apart from the main proposal.
It might be expected intuitively that Pirate A will have to allocate little if any to himself for fear of being voted off so that there are fewer pirates to share between. However, this is quite far from the theoretical result.
Which is ...
...
...
A: 98 coins
B: 0 coins
C: 1 coin
D: 0 coins
E: 1 coin
Proof is in the article linked. Amazing, isn't it? :-)
With the caveat that this 'proof' relies on the same assumptions that 'prove' that the rational prisoners defect in the one shot prisoners dilemma - which they don't unless they have insufficient (or inaccurate) information about each other. At a stretch we could force the "do not trust each other" premise to include "the pirates have terrible maps of each other" but that's not a realistic interpretation of the sentence. Really there is the additional implicit assumption "Oh, and all these pirates are agents that implement Causal Decision Theory".
It gets even more interesting when there are more than 200 pirates (and still only 100 coins).