Is there is a possibility for bargaining when you buy a new house in switzerland?
If it works then how much it could be?

Because of the actual housing shortage, there is probably no room to bargain if you realy want this house. Compare what is available on the market. But I would think you always could get better terms and conditions in your contract covering you in case the house which ist built has scarcities or will not be finished on time.

Depends how long its been on the market, but generally no. However you should be able to bargain on having extras thrown in e.g. better quality kitchen, bathroom or flooring, perhaps a discount on the parking place etc..

As mentioned in another post, I have recently bought an apartment. It was a new construction and I tried to bargain. The builder got another offer for the asking price and sold the apartment that I wanted (2nd floor). Later I had to settle for the 1st floor.

I have heard that it is easier to bargain on old apartments than new ones.

Hope this helps.

True. You have to be willing to lose it when you start negotiating.

I've negotiated on a couple of places and got them, and lost a quite a few too. When I saw my current home, I wasn't interested at all at the asking price and told them so. They said that there are loads of people interested, and I need to get back to them quickly. When they called me back a week later I knew there was some room for negotiation It ended up taking 6 months agree on price