In the Envelope game there are 2 players and 2 envelopes. One of the envelopes is marked ‘player 1’ and the other is marked ‘player 2’. At the beginning of the game, each envelope contains $1. The...

In the Envelope game there are 2 players and 2 envelopes. One of the envelopes is marked ‘player 1’ and the other is marked ‘player 2’. At the beginning of the game, each envelope contains $1. The game has three stages. In the first stage, player 1 must decide whether to ‘Stop’ or ‘Continue’. If he chooses ‘Stop’, then each player receives the money in their own envelope and the game stops. If he chooses ‘Continue’, then the $1 is removed from his envelope, and $2 is added to player 2’s envelope. In the second stage, player 2 must decide whether to ‘Stop’ or ‘Continue’. If she chooses ‘Stop’, then each player receives the money in their own envelope and the game stops. If she chooses ‘Continue’, then $1 is removed from her envelope, and $2 is added to player 1’s envelope. In the third stage, player 1 must again decide whether to ‘Stop’ or ‘Continue’. If he chooses ‘Stop’, then each player receives the money in their own envelope and the game stops. If he chooses ‘Continue’, then $1 is removed from his envelope, and $2 is added to player 2’s envelope. After this the game ends. a Draw the game tree that represents the Envelope game. b What is the roll-back equilibrium of the game?