If you have enough rubber mats, lay them out and tape them together using strong tape like duct tape. If the sides reach right to the walls, then it has nowhere to go.
Downside is that this mega-mat can still slide, especially if you turn sharply while walking, or brake a car/bike to a stop in the garage.
Given its a rental, bolting through into the concrete is probably undesirable, but if done properly could be accepted. You could put down a plywood floor layer and screw/glue the mats to that, would reduce the number of "mats" but still have the same fastening problem, or could use angle brackets to fasten the wooden subfloor to the garage wall bottom plates.
Another way would be to find a glue to stick the rubber mats straight to the concrete, and when it comes time to move out you tear the matt up and then use a chisel or paint scraper to remove any leftover. Small dots in each corner would be easier to clean than an enthusiastic slather of glue.