Answer Happy

(In this and all other questions in which a game matrix is given, Player 1 chooses the row, Player 2 chooses the column, and if there is a Player 3, she chooses the matrix.) Consider the following stage game which will be repeated an infinite number of times. A B A 4,-1 4,1 B 5,2 0,3 Player 1 begins by playing B. They then play B as long as Player 2 has only ever played A. Otherwise, they play A. Player 2 begins by playing A. They then play A as long as Player 1 has only ever Suppose the players adopt the following strategies: played B. Otherwise, they play B. What is the smallest value r can be if these strategies are to form a subgame Player 2 has discounting factor r, where 0 <= r <= 1. perfect Nash equilibrium? Round your answer to two decimal places.