The word collusion was first used in a 1397 Chaucer poem, where he spelled it collucione. After that, some early authors wrote it as collusyon or collusioun, but collusion became the standard fairly quickly. The word, which precedes the verb collude by over a century, traces to Old French collusion and Latin collusionem, which referred to the act of colluding. That comes from the verb colludere, which meant "play together" but in a legal context meant "to have a secret understanding" (here, "play" got extended to a greater sense of "cooperation"). The roots there are the prefix cum-, meaning "with" (and tracing to Proto-Indo-European kom, "next to") and ludere, which you may recognize from the words illusion, prelude, ludicrous, delude, and others as meaning "to play" (this might be from Etruscan).
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.