[Lewis Thomson (OP)]

Peter asks:

What would happen if two positrons collided?

What do you think?

[chiralSPO]

Same thing that happens when two electrons collide. There will likely be some EM radiation released (frequency depending on how fast their relative velocities are). https://en.wikipedia.org/wiki/Bremsstrahlung

[Kryptid]

If the energies of the two positrons are high enough, you could get a shower of new particles (just as long as the particles produced obey conservation laws, such as having a net charge equal to that of the two positrons).

[evan_au]

...but some really interesting things happen if a positron and an electron collide at a fairly low energy - the positron can act as a light proton, forming a very light pseudo-hydrogen nicknamed "positronium".

Unlike Hydrogen, it has a rapid and rather spectacular end.

See: https://en.wikipedia.org/wiki/Positronium