There is a switch and two capacitors behind. Low speed will switch the small one in series with the fan, medium will switch the big one in series, and high will bypass them completely.
You have two options –
1. Take the switch off the wall and look at the capacitor (they are in a single module) and note the capacitance and go to the local electrical wholesalers and buy a new one (with the understanding you can go smaller or larger to adjust the speed) and replace it.
2. Call the realestate agent. and get them to fix it.
Note: you can swap the capacitor with another that works in the house that you don’t use on low speed.