My bike is worth $M to me and $Y to you. Unless I buy a fancy lock that costs $F, you are able to take my bike.

Suppose that M > Y > F. Suppose that I have a property right over the bike. That is, you may not take the bike without my permission (or you'll go to jail for a million years). If there are no bargaining problems, what outcome do we expect?

I will pay you an amount between Y and M not to take the bike, and I will not buy the lock.

I will keep the bike, I will buy the lock, and no payments will be made.

I will keep the bike, I will not buy the lock, and no payments will be made.

You will pay me an amount between F and Y for the bike, and I will not buy the lock.

You will pay me an amount between Y and M for the bike, and I will not buy the lock.