Consider the following bargaining game with four rounds: Players 1 and 2 divide a pie of size 1. Both players have a common discount factor, δ = 0.8. In the first round (player 1 proposes): player 1 proposes x ∈ [0, 1]. If player 2 accepts the offer, then player 1 gets x, and player 2 gets 1−x. If player 2 rejects the offer, the game proceeds to round 2. In the second round (player 2 proposes): player 2 proposes y ∈ [0, 1]. If player 1 accepts the offer, then player 1 gets δy, and player 2 gets δ − δy. If player 2 rejects the offer, the game proceeds to round 3. In the third round (player 1 proposes): player 1 proposes z ∈ [0, 1]. If player 2 accepts the offer, player 1 gets δ2z, and player 2 gets δ2 − δ2z. If player 2 rejects the offer, the game proceeds to round 4. In the fourth and final round (player 2 proposes): player 2 proposes u ∈ [0, 1]. If player 1 accepts the offer, player 1 gets δ3u, and player 2 gets δ3 −δ3u. If player 1 rejects the offer, everyone gets 0. 1. What would be the SPNE of the game?
Consider the following bargaining game with four rounds: Players 1 and 2 divide a pie of size
1. Both players have a common discount factor, δ = 0.8.
In the first round (player 1 proposes): player 1 proposes x ∈ [0, 1]. If player 2 accepts
the offer, then player 1 gets x, and player 2 gets 1−x. If player 2 rejects the offer, the game
proceeds to round 2.
In the second round (player 2 proposes): player 2 proposes y ∈ [0, 1]. If player 1 accepts
the offer, then player 1 gets δy, and player 2 gets δ − δy. If player 2 rejects the offer, the
game proceeds to round 3.
In the third round (player 1 proposes): player 1 proposes z ∈ [0, 1]. If player 2 accepts
the offer, player 1 gets δ2z, and player 2 gets δ2 − δ2z. If player 2 rejects the offer, the game
proceeds to round 4.
In the fourth and final round (player 2 proposes): player 2 proposes u ∈ [0, 1]. If player
1 accepts the offer, player 1 gets δ3u, and player 2 gets δ3 −δ3u. If player 1 rejects the offer,
everyone gets 0.
1. What would be the SPNE of the game?
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