In Lexicon, you build a Wikipedia or SCP-style encyclopedia of a fictional world or event with collaborators. Although there is a leader who checks for outright contradictions, every participant equally contributes to the world, citing articles that have not been written yet, and eventually writing the articles cited by others.
I may write some more thoughts on the best ways to organize such a game, but for now:
This is the editing software that I use and plan to contribute to: https://github.com/Jaculabilis/Lexipython (But not required. A friend of mine played a modified version of this game using Google Drive rather successfully).
This is the first lexicon I participated in (I was Gustivus Pulluman): https://jaculabilis.github.io/site/lexicon/Draconium/contents/?byindex
This is the first lexicon I ran (amazingly, to completion, as Kelsey Khan): https://nickasabo.com/Lexicon/Xenocryst/contents/
This is the second lexicon I ran (which unfortunately fizzled out, as Holly Famous): https://nickasabo.com/Lexicon/Automata/contents/?byindex
This is the second lexicon I played (and did not run. As Dr. Naomi Imoan): https://jaculabilis.github.io/site/lexicon/Subtilis/contents/?byturn