Y'all know what a Dyson Tree is, i'm sure. The same physicist proposed another hypothetical - a Dyson Sphere
. (Personally, I knew about the sphere before I knew about the tree).
A Dyson Sphere is a structure built around a single star, designed in such a way as to capture as much energy as possible from that star. Most science fiction paints a Dyson Sphere as a closed, rigid structure, but the interpretation that Freeman originally intended was that a Dyson Sphere would be a large collection of loose objects - like asteroids, or satellites.
Given that Dyson Trees are likely to need sunlight in order to grow and do things, it would definitely be keeping within the theory to bundle your asteroids (and preferably, a lot of them) around a star. If you ever end up scaling the game to MMORPG levels, that is.
Also, it'll elevate the game from competing for single asteroids, to competing for asteroid belts, to competing for Dyson Spheres. Very ... galactic-dominationy, methinks.