>What solutions have been used for other 'sharing econom[ies]'?
Two things come to mind, rental cars and places like rent-a-center. To rent a car you have to give ID and a credit card, and if the car is stolen the police can and will be contacted. Whereas with rent-a-center they can't call the police, police don't deal well with "small" stolen items. Rent-a-centers employ call centers that harass the person into paying or retuning and calls family and friends to shame the person into paying. If that doesn't work they turn it over to a collections agency who has the power to continue to harass and even ruin someones credit.
I don't see something like this working P2P and in the startup space, it requires too much "infrastructure" if you will, to work and be successful in deterring and overcoming theft, loss and damage.