If you bid $2 you get at least $2 (you might get $4 if your partner bids above $2, but there’s no partner bid that can get you less than $2). If you bid anything more than $2, you might get $0, if the other party bids $2. Nash equilibrium is simply the state where no other-player-choice can reduce your payout.
If you’re trying to maximize average/expected payout, and you have some reason to believe that the other player is empathetic, super-rational, or playing a different game than stated (like part of their payout is thinking of themselves as cooperative), you should usually bid $100. Playing against an alien or an algorithm who you expect is extremely loss-averse and trying to maximize their minimum payout, you should do the same and bid $2.
If you bid $2 you get at least $2 (you might get $4 if your partner bids above $2, but there’s no partner bid that can get you less than $2). If you bid anything more than $2, you might get $0, if the other party bids $2. Nash equilibrium is simply the state where no other-player-choice can reduce your payout.
If you’re trying to maximize average/expected payout, and you have some reason to believe that the other player is empathetic, super-rational, or playing a different game than stated (like part of their payout is thinking of themselves as cooperative), you should usually bid $100. Playing against an alien or an algorithm who you expect is extremely loss-averse and trying to maximize their minimum payout, you should do the same and bid $2.