Yes, I understand that it's not relevant, but since we're talking about the game before the "Game Over" (GO) point, which is practically offline (without contact), we need conditions that are equal for everyone. And randomness will never provide such conditions.

Added after 26 minutes
Another raw idea, but maybe it will inspire someone: A mini-nostalgia game for 4 players (which also works well for a game with 3 players), each with their own computer, in a treasure hunt after the "Game Over" point, with a mini-treasure (of a specific type to avoid confusion, for example, sand) containing some object. The first player to take the object wins, and the remaining players continue to compete among themselves. This minimizes the likelihood of "alliances" and, at the same time, makes it quite likely that players will interact in the treasure hunt itself, which means it won't be "offline."