Crime victims have little economic incentive to punish the perpetrator; if you burn my house down, jailing you won’t un-burn the house. If you steal my gold, I have some interest in catching you and taking it back, but no more than I do in catching some other poor shmuck and taking his gold. It’s only society as a whole that wants to make sure criminals are reliably punished and the innocent consistently safe. This is the classic situation where economists usually recommend government intervention

Examples of different equilibria: