I have seen an advertisement for an apartment I'd consider but not what I am willing to pay for the offer. I would rent it if it was around 15% cheaper and wouldn't for this price. Have you ever heard of successful rental price negotiations in Switzerland?
I think a lot would depend on whether you think there is much competition for this flat, or if might it be difficult for the owner to find a tenant. If it's in a desirable location I'd say you don't have any negotiating power as someone will be willing to pay a premium, but if there are a few "downsides" that might make the apartment less desirable you might be able to strike a deal.
As a landlord almost every tenant tries to get something off, but for the studios its always a no as we have a waiting list for them.
Our one bedroom flats rent quite easily but if they ask then I agree to knock say CHF 50 or 100 off, but want something in return such as them paying the heating.
In the larger ones, likewise, but as they are up for sale they have to agree to allow reasonable access for viewing and a three month renewable contract.
Somehow we are fully rented and never advertise other than through our own website!