[UnquietTinkerer]

This is a good line of questioning. I believe that the difference between the two situations is that the pizza deal is implied to be just for Alice and Bob. If either walks away then the deal is totally sunk, so they both have equal "leverage" over the deal.

When you frame it as an investment question, the implication is that if either person walks away then they can be replaced by a third party who is willing to stake the cash. Since it is easier to replace someone when their stake is lower, the person putting up the $2k has less leverage in this case.

If you explicitly limited the investment to two specific people (imagine a crazy term in a will or something), then I think you'd end up back with a $7k/$5k split.

[beowulfey]

Definitely agree, a big part of this is also how badly the person putting more into it needs that other partner.