When min-max is wrong

rjlipton.wordpress.com

14 pointsTriinT6 comments

If you convert the dollar amounts to the actual value that the players will experience, then the problem dissolves.

Adjusting for the marginal utility of dollars at various levels of wealth should make this whole problem a non-issue. Am I missing something?

I'm sure that losing $X, where X is large compared to your wealth, is generally a bigger event than gaining $X in terms of utility. But can't we always repeat the argument so that the game is fair when measured in utility?

Yes, but once you've done so the problem loses the property of having one set that is preferable to the others.

It's also generally impossible to make a non-trivial game both zero sum in dollars and zero sum in utility, when using a non-trivial dollar->utility conversion.

A little off-topic, but it's made my day seeing one of Lipton's posts on the front page.

It only started relatively recently and it's been a really good computational complexity blog so far.

Yeah, I have to agree. It does a wonderful job of doing very loving mini expositions on a whole slew of topics, and doing so at regular intervals!

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