DING DING DING!!! Everybody upvote this guy! Yep, that's the answer I was hoping somebody would give. Ignoring your "conscience-value" ci is the trick that lets us claim uniqueness of Nash Equilibria, which makes the result sound much more convincing than it should be.

I don't have time to think about it now, but it might be interesting to see if including ci could lead to anything weird, unexpected, or perverse. I'm fairly certain that in the simple two-choice model, ci would only make our equilibria look better, but sometimes these things can surprise.