1 Three players, P1, P2, and P3, bargain for shares of a pie. Athree sided die is cast. If the die comes up number "j" thenPj gets to propose a split of the pie among the threeplayers. Once a proposal is made, the other playerssimultaneously accept or reject the proposal. If eitherresponder rejects then the game is over. If both playersaccept then the proposal is implemented and the gameends.For example, if shares of the pie 1/2 to P1, 1/4 to P2, 1/4to P3 are offered and this is accepted by the tworesponders then P1 gets a payoff of 1/2, P2 gets 1/4 and P3gets 1/4. An offered share to a player can be any numberbetween o and 1.There is an SPE of this game where one responder gets oand the other responder gets the whole pie, and theproposer gets o.1) True2) FalseThere is an SPE of this game where oneresponder gets 0 and the other responder getsthe whole pie, and the proposer gets 0. True orFalse?

The game theory is a logical methodology/analytical approach through which vital/strategic decisions…

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

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

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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Question

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
There is an SPE of this game where one
responder gets 0 and the other responder gets
the whole pie, and the proposer gets 0. True or
False?

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