Normally, you have two days to make a request and then 3 days to wait for anwser. But you can react quicker, especially, if the guest refuses. If you are still negotiating by mail, you need to put a request via the resolution center nevertheless.
You can write via airbnb mail at the beginning about the problem. Then, when the negociation goes on with back and forth messages but never anything definite, you write that you will send them the request via the approbriate form, and the amount will be X for the broken item, Y for shipping, Z for the repairman etc, amounting to a total of xxx. He has to accept that message.
Then you send the form via the resolution center. If he accepts, you are paid in that instant. If he comes back with something "It's too expensive, it's only worth 70 %", you can change your request (to 80 %) and resend.
If he says, he will not pay or that it is worth only 20 %, you click on the buttom to involve airbnb. If there is no anwser, I'd say you relaunce him after 20 hours and send the mediation request after 24 hours after the resolution demand.
That way, you do not miss deadlines and things don't go on for eternities.
Make it very clear, have a cost estimation and pictures ready and send it.
It depends on the worth of the item, but if the lamp is not Murano glass or Tiffanies, it's probably not worth all the bother. I don't ask for small stuff. Some eat breakfast, some don't, some heat like for a sauna and others nearly don't use electricity, some break a few things, others buy a few things, in the end, it's the average that needs to be calculated in your prices.
If the damage is considerable in relation to the total rent, you need to do things fast and sober, either they say yes or it's a disguised
way to say no, to let you loose time. Maybe they read the whole helpfiles and conditions on damages after breaking the lamp.
You should, anyway.
You can try to shame them into paying a bit over the resolution center or consider it a lesson learned.
Good luck and no more damages !
