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Three players, P1, P2, and P3, bargain for shares of a pie. A three sided die is cast. If the die comes up number "j" then Pj gets to propose a split of the pie among the three

Three players, P1, P2, and P3, bargain for shares of a pie. A three sided die is cast. If the die comes up number "j" then Pj gets to propose a split of the pie among the three

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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Three players, P1, P2, and P3, bargain for shares of a pie. A three sided die is cast. If the die comes up number "j" then Pj gets to propose a split of the pie among the three players. Once a proposal is made, the other players simultaneously accept or reject the proposal. If either responder rejects then the game is over. If both players accept then the proposal is implemented and the game ends. For example, if shares of the pie 1/2 to P1, 1/4 to P2, 1/4 to P3 are offered and this is accepted by the two responders then P1 gets a payoff of 1/2, P2 gets 1/4 and P3 gets 1/4. An offered share to a player can be any number between o and 1. There is an SPE of this game where one responder gets o and the other responder gets the whole pie, and the proposer gets o. 1) True 2) False
Transcribed Image Text:Three players, P1, P2, and P3, bargain for shares of a pie. A three sided die is cast. If the die comes up number "j" then Pj gets to propose a split of the pie among the three players. Once a proposal is made, the other players simultaneously accept or reject the proposal. If either responder rejects then the game is over. If both players accept then the proposal is implemented and the game ends. For example, if shares of the pie 1/2 to P1, 1/4 to P2, 1/4 to P3 are offered and this is accepted by the two responders then P1 gets a payoff of 1/2, P2 gets 1/4 and P3 gets 1/4. An offered share to a player can be any number between o and 1. There is an SPE of this game where one responder gets o and the other responder gets the whole pie, and the proposer gets o. 1) True 2) False
Three players, P1, P2, and P3, bargain for shares of a pie. A three sided die is cast. If the die comes up number "j" then Pj gets to propose a split of the pie among the three players. Once a proposal is made, the other players simultaneously accept or reject the proposal. If either responder rejects then the game is over. If both players accept then the proposal is implemented and the game ends. For example, if shares of the pie 1/2 to P1, 1/4 to P2, 1/4 to P3 are offered and this is accepted by the two responders then P1 gets a payoff of 1/2, P2 gets 1/4 and P3 gets 1/4. An offered share to a player can be any number between o and 1. There is an SPE of this game where the proposer gets 1 and the responders get 0. 1) True 2) False
Transcribed Image Text:Three players, P1, P2, and P3, bargain for shares of a pie. A three sided die is cast. If the die comes up number "j" then Pj gets to propose a split of the pie among the three players. Once a proposal is made, the other players simultaneously accept or reject the proposal. If either responder rejects then the game is over. If both players accept then the proposal is implemented and the game ends. For example, if shares of the pie 1/2 to P1, 1/4 to P2, 1/4 to P3 are offered and this is accepted by the two responders then P1 gets a payoff of 1/2, P2 gets 1/4 and P3 gets 1/4. An offered share to a player can be any number between o and 1. There is an SPE of this game where the proposer gets 1 and the responders get 0. 1) True 2) False
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