On Thu, May 21, 2020 at 7:11 PM Heather Madrone <heat...@madrone.com> wrote:

> In game theory terms, it's great if everyone cooperates, but you need a
> strategy to cope with serial defectors, too.
>

A few years ago, Dyson and Press published a paper[1] that showed that
generosity and extortion are finely balanced in populations. There were a
bunch of visualisations and simulations from various perspectives: cynical,
optimist, stoic and this one[2] which was widely shared at the time, mainly
because it looks nice. It basically explores tit-for-tat strategies.

This reminds me of Ian Stewart's column in the Scientific American from May
1999:

The logic of mathematics sometimes leads to apparently bizarre conclusions.
The rule here is that if the logic doesn't have holes in it, the
conclusions are sound, even if they conflict with your intuition. In
September 1998 Stephen M. Omohundro of Palo Alto, Calif., sent me a puzzle
that falls into exactly this category. The puzzle has been circulating for
at least 10 years, but Omohundro came up with a variant in which the logic
becomes surprisingly convoluted. First, the original version of the puzzle.
Ten pirates have gotten their hands on a hoard of 100 gold pieces and wish
to divide the loot. They are democratic pirates, in their own way, and it
is their custom to make such divisions in the following manner: The
fiercest pirate makes a proposal about the division, and everybody votes on
it, including the proposer. If 50 percent or more are in favor, the
proposal passes and is implemented forthwith. Otherwise the proposer is
thrown overboard, and the procedure is repeated with the next fiercest
pirate. All the pirates enjoy throwing one of their fellows overboard, but
if given a choice they prefer cold, hard cash. They dislike being thrown
overboard themselves. All pirates are rational and know that the other
pirates are also rational. Moreover, no two pirates are equally fierce, so
there is a precise pecking order-and it is known to them all. The gold
pieces are indivisible, and arrangements to share pieces are not permitted,
because no pirate trusts his fellows to stick to such an arrangement. It's
every man for himself. What proposal should the fiercest pirate make to get
the most gold? For convenience, number the pirates in order of meekness, so
that the least fierce is number 1, the next least fierce number 2 and so
on. The fiercest pirate thus gets the biggest number, and proposals proceed
in reverse order from the top down.

Full column here[3].

Footnotes:
[1] https://pubmed.ncbi.nlm.nih.gov/22615375/
[2] https://ncase.me/trust/
[3]
https://omohundro.files.wordpress.com/2009/03/stewart99_a_puzzle_for_pirates.pdf

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