## Mediated envy-free and efficient cake cutting with n=2?

Is there an algorithm in literature to compute an efficient (pareto optimal) and envy free cake cutting when there are only n=2 players and a Mediator?

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 Will Mediator work for free? – Ilya Nikokoshev Dec 24 2009 at 13:22 I suggest you add the "fair-division" tag to the question. – Joel Reyes Noche Mar 30 2011 at 1:44

Huh? I cut, you choose. Why do we need a Mediator?

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I suspect that "envy-free" might rule this out, though I don't know what assumptions are going into this, or what "envy-free" means in a technical sense. Perhaps if I'm bad at cutting, then I will envy you for getting the bigger piece? The use of an undefined technical term like this from economics makes the question sound like a homework question. – Kenny Easwaran Oct 22 2009 at 14:40
>Perhaps if I'm bad at cutting, then I will envy you for getting the bigger piece? And what if you're bad at choosing? Then it's hopeless! I think your objection is silly. – TonyK Oct 22 2009 at 14:54
That didn't work very well :-( I meant to quote Kenny, and add further commentary,but comments don't parse like answers do... – TonyK Oct 22 2009 at 14:55
Cut and choose is not pareto optimal, which is: there could be a better assignment that makes some of the players better off without making anybody worse off. This is the case, because in the cut and choose method, the person that cuts is guaranteed to have 1/2 of it view of the cake, whereas the person the chooses get at least one half. – unluckyjoe Oct 23 2009 at 0:36
That doesn't make sense to me, whatever '1/2 of it view of the cake' means. Any improvement for the cutter is necessarily worse for the chooser. So why isn't it Pareto optimal? On an unrelated note, if the cutter can't be trusted to look after their own interests, we don't seem to have anything to go on at all! (And in the real world, of course, 'envy-free' is an impossible goal...) – TonyK Oct 24 2009 at 11:26

Take a look at: