Also, imagine you are playing the game against someone you think is rational. You are Player 2. You are told that A was not picked. What do you do?

If I think Player 1 is rational, I assume he must be modeling my decision-making process somehow. If his model of my decision-making process has picking B or C seems rational, he must be modeling my choice of X and Y in a way that gives him a chance of a higher payoff than he can get by choosing A. Since every combination of (B,C) and (X,Y) is lower than his return from A except [C,Y], no model of my decision-making process would make B a good option, while some models (though inaccurate) would recommend C as a potentially good option. So while it's uncertain, it's very likely I'm at C. In that case, I should pick X, and shake my head at my opponent for drastically discounting how rational I am, if he thought he could somehow go one level higher and get the big payoff.