It is a kind of emergent game where you can only know the rules by playing the game and by an unspoken, but somehow mutual agreement with the other players.
Here are a few of the rules that I learned:
1. It's a two-person game. You can only play with one other player at a time.
2. You challenge an opponent by looking them in the eyes and not looking away at the point where you would be expected to do so. The other player accepts the challenge by not averting their gaze. If they don't want to play, they will look away or ignore you. In either case, they will make their intention clear very quickly. It takes maybe a couple of seconds for all this to transpire.
3. You win if you keep your gaze fixed until the other player looks away.
4. The game is a draw if the other player is forced to look away, for example because it's their stop, or another passenger demands their attention etc.
5. If eye contact is interrupted, for example because people come and stand between the players, the result is undefined. If contact is re-established, a new game must be initiated by one of the players challenging the other all over again.
6. If the other player behaves aggressively, tries to ridicule the opponent, or otherwise tries to disrupt the opponent's gaze, they are disqualified. The only contact between the players must be gazing into each other's eyes.
7. Blinking is allowed, but excessive blinking may be cause for disqualification.
8. It is fine to challenge a player after losing a first round. I found that in that case there is a heavy psychological penalty, though and I usually lost again in that situation.
9. It is a game played by men. A man staring at a woman's eyes can be creepy or scary and so it is hard to make a fair challenge. I've never seen two women play. On the other hand, I also never saw two men play when I wasn't one of them.
Those are the rules I remember. This was a long time ago, and perhaps the rules would have changed now that I'm not a young man anymore.
I became quite good at the game, although I was not undefeated. I played for a couple of years, primarily on long train rides that lasted half an hour or more.
I have not played the game for many years now.