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Consider a bargaining game with T = ∞ rounds of bargaining. At the beginning of each round the proposer makes an offer to split a surplus of size 1. If the responder accepts, the offer is executed, and the game ends with the

Consider a bargaining game with T = ∞ rounds of bargaining. At the beginning of each round the proposer makes an offer to split a surplus of size 1. If the responder accepts, the offer is executed, and the game ends with the

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Consider a bargaining game with T = ∞ rounds of bargaining. At the beginning of each round the proposer makes an offer to split a surplus of size 1. If the responder accepts, the offer is executed, and the game ends with the payoffs determined by the offer. If the offer is rejected, the game moves on to the next round, except in the last round, where the game ends after rejection. If the game ends without agreement then both players getting zero. Here is the twist. The role of proposer and responder in each round is determined randomly. At the beginning of each round a fair coin is tossed. If it comes up heads P1 proposes in that round. If the toss comes up tails then P2 proposes in that round. Assume offers can be any number. Notice there is no shrinking pie. Consider an SPE of the game. In the equilibrium, what is first offer made by the first proposer?
Transcribed Image Text:Consider a bargaining game with T = ∞ rounds of bargaining. At the beginning of each round the proposer makes an offer to split a surplus of size 1. If the responder accepts, the offer is executed, and the game ends with the payoffs determined by the offer. If the offer is rejected, the game moves on to the next round, except in the last round, where the game ends after rejection. If the game ends without agreement then both players getting zero. Here is the twist. The role of proposer and responder in each round is determined randomly. At the beginning of each round a fair coin is tossed. If it comes up heads P1 proposes in that round. If the toss comes up tails then P2 proposes in that round. Assume offers can be any number. Notice there is no shrinking pie. Consider an SPE of the game. In the equilibrium, what is first offer made by the first proposer?
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