ayer 1 and Player 2 are trying to agree on how to split a pie of size 1 in a two-stage bargaining game. If no agreement is reached after the two stages are complete, the pie is split for them according to a pre-arranged agreement that gives Player 1 and Player 2 one-quarter and three quarters of the pie, respectively. In the first stage, Player 1 makes an offer (x1, x2), where x1 + x2 = 1. Player 2 can either accept this offer (at which point the game ends and the pie is split according to Player 1’s offer), or can make a counter-offer. When Player 2 makes a counter offer, Player 1 can either accept (in which case the pie is split according to Player 2’s offer) or can reject, in which case the pie is split according to the pre-arranged agreement. Both players have a discount factor d – getting dx in the first stage (after Player 1’s proposal) is as good as getting x in the second stage (after Player 2’s proposal). a) In the last stage of the game, Player 1 will accept any offer giving him ≥ _____. Therefore Player 2 would offer ____ to Player 1 and get ____ for himself. b) In the SPNE of this game, Player 1 gets ____ and Player 2 gets _____
Player 1 and Player 2 are trying to agree on how to split a pie of size 1 in a two-stage bargaining game. If no agreement is reached after the two stages are complete, the pie is split for them according to a pre-arranged agreement that gives Player 1 and Player 2 one-quarter and three quarters of the pie, respectively. In the first stage, Player 1 makes an offer (x1, x2), where x1 + x2 = 1. Player 2 can either accept this offer (at which point the game ends and the pie is split according to Player 1’s offer), or can make a counter-offer. When Player 2 makes a counter offer, Player 1 can either accept (in which case the pie is split according to Player 2’s offer) or can reject, in which case the pie is split according to the pre-arranged agreement. Both players have a discount factor d – getting dx in the first stage (after Player 1’s proposal) is as good as getting x in the second stage (after Player 2’s proposal).
a) In the last stage of the game, Player 1 will accept any offer giving him ≥ _____.
Therefore Player 2 would offer ____ to Player 1 and get ____ for himself.
b) In the SPNE of this game, Player 1 gets ____ and Player 2 gets _____
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