You can’t define a modal agent that swerves if and only if the other player doesn’t swerve, because “the other player doesn’t swerve” is not a modalized formula.
CarefulBot does not seem much like FairBot to me. It also seems undeserving of its name, since it doesn’t swerve unless it can prove that the other player won’t. Perhaps instead you should make it so it swerves unless it can prove that the other player does?
You can’t define a modal agent that swerves if and only if the other player doesn’t swerve, because “the other player doesn’t swerve” is not a modalized formula.
CarefulBot does not seem much like FairBot to me. It also seems undeserving of its name, since it doesn’t swerve unless it can prove that the other player won’t. Perhaps instead you should make it so it swerves unless it can prove that the other player does?