Find the pure-strategy Bayesian Nash equilibrium in the following static Bayesian game:

(1) Nature determines whether Game 1 or Game 2 is going to be played, with each game being equally likely;

(2) Player 1 learns whether nature has drawn Game 1 or Game 2, but player 2 does not;

(3) Player 1 chooses either T or B depending on what nature has drawn, and player 2 simultaneously chooses either L or R;

(4) Payoffs are given by the game drawn by nature (see the tables below).

Game 1: Game 2: L R L R T 2, 2 1, 0 T 0, 0 0. 0 B 0, 0 0, 0 B 1, 0 3. 3