I don't offer additional discounts as my prices are more than reasonable for London and for what the guests are getting. I usually just explain to them that they are paying around the same price as a private room in a not so nice hostel. I've never had a guest ask twice. If they do a tiny bit of research they will see I'm right!
Are guests who ask for discounts going to be problem guests? Sometimes. Recently I had guests ask for the weekly discount even though they were staying for less than a week. I said no. They then wanted to check in at 10 am instead of my normal 3 pm time. I said no. They showed up at 9.30 am anyway. Then they wanted to use my washing machine straight away (clearly stated in my rules as not available to short term guests) and so it went on...
On the other hand, I've had long term guests ask for a reduction not realising that weekly and monthly discounts are already in place. One of these ended up staying with me for four months and was lovely. I'm glad I didn't decline him just because he intially asked for a discount.
I sometimes also get enquiries from guests who don't understand that they are paying Airbnb fees. They ask why the price jumped from £X in the listing to £Y when they wanted to book. Can I give them the initial price quoted on the listing? Then I have to explain how the whole darn thing works...