Not sure if accepting $1 is perfectly rational. Unless you ignore the fact that other player is a human. Otherwise you know, that if they can win more and if yo

Not sure if accepting $1 is perfectly rational. Unless you ignore the fact that other player is a human. Otherwise you know, that if they can win more and if you do not cooperate they will pass much bigger opportunity you can very well assume that they will be willing to pay way more than just one $1. Supply and demand.