Good thinking, but I picked the payoffs so this approach wouldn’t give an easy solution. Consider an equilibrium where Player 1 intends to pick A, but there is a small but equal chance he will pick B or C by mistake. In this equilibrium Player 2 would pick Y if he got to move, but then Player 1 would always intend to Pick C, effectively pretending he had made a mistake.
From Fudenberg & Tirole (1995 edition, chapter 8):
Section 8.4 then describes a refinement of trembling-hand perfect equilibrium due to Myerson(1978). A “proper equilibrium” requires that a player tremble less on strategies that are worse responses.
Good thinking, but I picked the payoffs so this approach wouldn’t give an easy solution. Consider an equilibrium where Player 1 intends to pick A, but there is a small but equal chance he will pick B or C by mistake. In this equilibrium Player 2 would pick Y if he got to move, but then Player 1 would always intend to Pick C, effectively pretending he had made a mistake.
From Fudenberg & Tirole (1995 edition, chapter 8):