Big thanks to the LW team for putting together the Petrov Day experience! (Setup. Follow up.)
I looked over the comments and it seems like there there were a number of suggestions for how to do this better. Instead of waiting for the next year, let's do it right now.
My proposed setup:
1. Take the original 125 LW users. Take a prize pool of $1,250 (or more if people are willing to donate). The prize pool is split evenly between each player, but you have to survive the game to get paid. Everyone is anonymized in the game.
2. The game will last a minimum of 4 days (to give everyone enough time to act, strategize, and think). After 4 days, there will be an increasing probability that the game will end at any minute. (This is to prevent anyone trying to attack right when the game ends to avoid retaliation. In expectation, the game should last about a week.)
3. Each player will have the number of missiles equal to the number of players. They can launch any number of them.
4. When a missile is launched: a) the attacked player is notified that they are being attacked by a specific player (and therefore has an option to retaliate), b) 48 hours after the launch, the attacked player is declared dead: they can no longer perform any actions and will not receive a payout, c) 48 hours after the launch, the attacking player gets the target player's entire prize pool.
5. During the game there will be at least 125 fake alerts. They will be generated randomly (so some players might receive zero or more than one fake alerts). It will look the same as if some specific player has launched a missile against you. 48 hours after the notification, you'll find out whether it was real or not by whether or not you're still alive.
What do you think?
It looks like you get a big advantage from sharing information with another player. In the absence of this, maybe the best strategy is to respond to all alerts with some probability that you think leads to good dynamics if adopted as a general strategy.
What information would you share that would give you an advantage? (Keep in mind that players are anonymous. Though I guess anyone could in theory de-anonymize themselves.)
Well, if players still have identifying pseudonyms, you could share that you're being attacked by a certain pseudonym to help you update on whether attacks are real or false, you could try to coordinate to not attack each other if you know your own psudonym. But even without pseudonames, you could share timing information, which might be important.
I guess that seems to me to be within the spirit of the game.