If Player One believes that Player Two is going to pick Y, then Player One will pick C, but of course this isn’t an equilibrium since Player Two would regret his strategy. All Player Two ever sees is Player One’s move, not the probabilities that Player 1 might have used so if C is played Player Two doesn’t know if it was because Player One Played C with probability 1 or probability 2/3-ϵ.
If Player One believes that Player Two is going to pick Y, then Player One will pick C, but of course this isn’t an equilibrium since Player Two would regret his strategy. All Player Two ever sees is Player One’s move, not the probabilities that Player 1 might have used so if C is played Player Two doesn’t know if it was because Player One Played C with probability 1 or probability 2/3-ϵ.
Perhaps Player One figures that Player Two knows enough about him to predict him slightly more than explainable by chance, and vice versa.