What's the deal with renting prices?
I know when people sell a house, they put the asking price x% amount higher than they would accept.
Is it the same when they rent out their place? Is it normal to offer less or the asking amount?
The definitive answer to that is that there is no answer to that. Some landlords might or will accept an offer, while others will reject potential tenants for the reasons TheCrow gave. A lot will depend on the type and location of property, the type of landlord and localised market conditions.
As an ex-landlord, I hated to see empty property but not as much as I hated to have awkward tenants, and I agree with TheCrow that attempting to negotiate might suggest a tenant that will struggle to find the rent, and that suggests awkward tenant. Or, it might just mean someone with an eye to a deal.,
I wouldn't reject a tenant just for that, but it would be a tick in the negative column.
On the other hand, my policy was that after a period of tenancy and having had no problems, I'd offer a non-binding goodwill reduction on rent. If you like, a No Hassle Discount, conditional on continued no-hassle, like a car insurance discount. Reporting of legitimate problems did not constitute hassle, and would be dealt with without impacting that discount. The discount was really an inducement to keep regular, hassle-free tenants because it helped insure a regular income stream, and avoided any between-tenant drops in income stream.
The only way I'd entertain "negotiation" was after a protracted period of non-letting, which told me either something about the property was wrong, in which case it needed finding and correcting, or my expectation was off.
However, all this was not in the UK so quite how it works here, I don't know.