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  A Theorem on Finite Abelian Groups

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  The Prisoner's Dilemma
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You know that old saying, “you can't cheat an honest man”? I like it, and have certainly found it to be true in my experience. Damn those honest men!

The reason I mention it is, I just realized it is very close in meaning to something I said above (in Game Theory):

… what game theory tells you is that if you choose randomly, and give up trying to exploit the other player, then you also can't be exploited.

So, what we have here is a proverb with a mathematical basis. That is unusual! Or, to put it another way, we have a mathematical definition of honesty. The method of game theory is often described as minimizing your losses rather than maximizing your gains, which doesn't sound much like honesty, but it can also be described as trying to obtain neither more nor less than the fair value.

Not accepting less than the fair value is important. In terms of the iterated prisoner's dilemma, if you think of honesty as always telling the truth, it's easy to mistakenly map it onto the strategy AC (always cooperate). That's not what you want; what you want is the stern retaliatory honesty of TT (tit for tat).

Finally, another thing I said above, namely,

… the best strategy, from a game-theoretic point of view, may not be much fun.

reminds me of a funny thing from Undercut, Flaunt, Pounce, and Mediocrity.

In an article in the British journal Manifold titled “A Pandora's Box of non-Games”, Anatole Beck and David Fowler set forth a panoply of rather silly games that are halfway between true games and pure jokes. … For instance, consider the game they call Finchley Central:

Two players alternate naming the stations on the London Underground. The first to say ‘Finchley Central’ wins. It is clear that the ‘best’ time to say ‘Finchley Central’ is exactly before your opponent does. Failing that, it is good that he should be considering it. You could, of course, say ‘Finchley Central’ on your second turn. In that case, your opponent puffs on his cigarette and says, ‘Well, … ’ Shame on you.

* * *

In addition to Finchley Central, there's also Mornington Crescent. I've heard about it a couple of times now, but I keep forgetting the name, so I thought I'd make a little note here. I won't try and explain the rules; you can look them up for yourself if you want.


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@ June (2003)
o April (2009)