Background
I have (rather recently) dabbled in game theory. I need it to design an algorithm to share chores. Obviously this is a kind of cake-cutting problem. So far, I have fought my way through An Introduction to Game Theory by Martin J. Osborne, but I'm still feel far from comfortable with it. I have a solid foundation in calculus, know how to deal with ODEs and PDEs (but I try to avoid them if I can. :)
) And yes, I'm not a mathematician, I"m an engineer.
Problem
The 'cake' needs to be split among $k\geq 2$ players. The twist is that valuation of the players is not finitely additive, it has a maximum i.e. there is an amount of cake that they will find more valuable than a larger amount (kind of being afraid of overeating $-$ or being on a diet).
Question
Does anybody know of a starting point to how tackle this? (Efficient or equitable solutions would be the most interesting.) All the resources I found, treat only the finitely additive case. I would also be grateful for any freely downloadable material.
EDIT: I'm looking for efficient and/or equitable ways of splitting the cake, regardless of the protocol to achieve it. If there also is a protocol for that, the better for me. :)