How do I define an ideal customer for a two-sided marketplace where I have to pick two of them?

In a marketplace you have two ICPs, but they are not equal partners: pick the harder side to attract as your anchor and define it precisely first. Usually supply is scarcer or pickier, so nail the ideal supplier profile, then define the demand side that specifically wants what that supply offers. Trying to define both broadly at once gives you a thin, unmatched marketplace, so start narrow enough that a supplier and a buyer can actually find each other in one city or one category. Treat the constrained side as the one that shapes everything, and refine from your earliest real matches.