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6. Two players play the following bargaining game. The game is played over two periods. Period 1: Player 1 makes an offer m =
6. Two players play the following bargaining game. The game is played over two periods. Period 1: Player 1 makes an offer m = [0,1]. After observing the offer, player 2 decides whether to accept or reject. If player 1's offer is accepted, the game ends with player 1 receiving 1 m and player 2 obtaining m. If player 2 rejects the offer, then game proceeds to the second period. Period 2: Player 2 makes a counteroffer m2 [0,1], which player 1 either accepts or rejects. If player 1 accepts player 2's offer, then player 1 gets dm2 and player 2 gets 62 (1 m2) as their final payoffs, where d = (0,1) and 82 (0,1) represent their discounting factors. If player 1 rejects player 2's offer, then the game ends and each player obtains Siwi 0. We assume w + w < 1. Note that the subgame played in the second period is essentially identical to the game considered in the previous question, with the roles of the two players reversed. Find the subgame perfect Nash equilibrium of this game.
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