Every player has landed on the moon, searching for resources.
The English subordinate clause gives a reason, this can be translated into German in different ways:
Jeder der Spieler ist auf dem Mond gelandet, um nach Bodenschätzen zu suchen.
A subordinate clause with um … zu is the typical way to give a reason.
Jeder der Spieler ist zum Suchen nach Bodenschätzen auf dem Mond gelandet.
Instead of a clause, the action suchen may be turned into a noun and the reason is given as a prepositional object with zu+dative or wegen+genitive.
A more free, but much better sentence however would be
Alle Spieler sind wegen der Bodenschätze zum Mond aufgebrochen.
That is because the reason "searching for resources" is clearly not connected to the action of landing but it was the incentive for the whole trip.