In the U.S., deductible cost and if the person with the damaged vehicle pays it, is driven by collision, comprehensive, uninsured motorists, and each particular plan. Even if the other driver is at fault, the owner of the car struck will more than likely pay the deductible. Some are lucky if their insurance company will do what is called deductible recovery via Subrogation where the insurance goes after the other company to reclaim damages, if successful, then the driver will most likely get their deductible returned. Regardless, the non-fault driver will quite often pay that deductible up front if they want their car repaired quickly. Waiting on the other insurance company to take responsibility may take months. This of course has a lot to do with the insurance company.
This is why I go with a $100 or $200 dollar deductible on my cars. Any car you need to take to a body shop will almost never coast you less the $600 dollars,and usually a lot more. Getting the low deductible only costs me something like $60 a year and is worth it.