Hmm, I just realized that Player Two’s strategy in the Nash equilibrium of this modified game is different than in the proper equilibrium of the original game. Because here Player Two has to make his choice so that Player One is indifferent between A and C, whereas in the proper equilibrium Player Two has to make his choices so that Player One is indifferent between B and C.
I think my “intuitive analysis” does make sense, so I’m going to change my mind and say that perhaps proper equilibrium isn’t the right solution concept here...
Hmm, I just realized that Player Two’s strategy in the Nash equilibrium of this modified game is different than in the proper equilibrium of the original game. Because here Player Two has to make his choice so that Player One is indifferent between A and C, whereas in the proper equilibrium Player Two has to make his choices so that Player One is indifferent between B and C.
I think my “intuitive analysis” does make sense, so I’m going to change my mind and say that perhaps proper equilibrium isn’t the right solution concept here...