This is a short story I read in the late 80s or early 90s in an anthology or collection.
Here are the plot points I remember:
- A human spaceship encounters a ship with hostile aliens (HA). There may be friendly aliens (FA) on board the human spaceship
- A human (or perhaps FA) telepath scans the HA and finds they are hostile and bent on conquest of other races
- The captain and crew decide on a bluff: pretend they are from a large federation of many species, one so big the HA will become discouraged and drop their plans of conquest
- They invite one or more HA on their ship
- To pretend that there are many (more) races in their federation, they do things like put a fake control panel in the ships aquarium and claiming the fish in them are one of the races in their federation
- The HA can't conceive of multiple races cooperating and are convinced there must be some race on top controlling it all. If not, they can just be conquered one at a time
- This goes on for a little while until, seeing their plan isn't working (via their telepath) the humans change their plan so that when
the ship's cat (so far unseen by the HA) walks in the room, one of the humans loudly calls "The CAT!" causing everyone to stand rigidly at attention while the cat walks around more or less ignoring everyone and everything the way cats do. Having seen the "top dog" and the rigid discipline and fear he instills in everyone else, the aliens "realize" the humans are deluded into thinking all races are equal members in their 'federation", the cats are really in control of a huge empire, and they should not be messed around with.