Problem 3. Val and Earl are at work on a very hot afternoon. There is a job waiting for them. It takes only one person to do the job. The one who does it must crawl through a mucky culvert to connect a pipe. Once the pipe is connected, they can both go to a comfortable tavern for a beer. The game tree is shown below, where at the terminal nodes, the top number is Val's payoff and the bottom number is Earl's payoff. Val Do it tall V 5 E 10 Earl Do it Stall Val Do it Stall 3 8 Earl Do it Stall Val Do it Stall Earl Do it Leave it At the beginning of play, Earl is working on another job, but Val could do the job and if he does it right away, they can both go out for beer. Val could choose to stall, waiting for Earl to come back. If Val decides to stall, then when Earl gets back, he could do the job, or he could stall. If Earl chooses to stall, Val could either do the job, or stall again, and so on... If Val and Earl both stall until Earl's final decision node at the end of the workday, Earl can either do the job, or they can both leave the job undone. The payoffs to both from leaving the job undone are given by the variable X. C) Find the subgame perfect Nash equilibrium profile if X < 0. In this equilibrium, who if anyone, does the job? Explain your answer. D) Find the subgame perfect Nash equilibrium profile if 0 < x < 1. In this equilibrium, who if anyone, does the job? Explain your answer. E) Find the subgame perfect Nash equilibrium profile if 1 < x < 2. In this equilibrium, who if anyone, does the job? Explain your answer.

Understanding Business

12th Edition

ISBN:9781259929434

Author:William Nickels

Publisher:William Nickels

Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment

Section: Chapter Questions

Problem 1CE

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Transcribed Image Text:Problem 3. Val and Earl are at work on a very hot afternoon. There is a job waiting for them. It takes only one person to do the job. The one who does it must crawl through a mucky culvert to connect a pipe. Once the pipe is connected, they can both go to a comfortable tavern for a beer. The game tree is shown below, where at the terminal nodes, the top number is Val's payoff and the bottom number is Earl's payoff. Val Do it tall V 5 E 10 Earl Do it Stall Val Do it Stall 3 8 Earl Do it Stall Val Do it Stall Earl Do it Leave it At the beginning of play, Earl is working on another job, but Val could do the job and if he does it right away, they can both go out for beer. Val could choose to stall, waiting for Earl to come back. If Val decides to stall, then when Earl gets back, he could do the job, or he could stall. If Earl chooses to stall, Val could either do the job, or stall again, and so on... If Val and Earl both stall until Earl's final decision node at the end of the workday, Earl can either do the job, or they can both leave the job undone. The payoffs to both from leaving the job undone are given by the variable X. C) Find the subgame perfect Nash equilibrium profile if X < 0. In this equilibrium, who if anyone, does the job? Explain your answer. D) Find the subgame perfect Nash equilibrium profile if 0 < x < 1. In this equilibrium, who if anyone, does the job? Explain your answer. E) Find the subgame perfect Nash equilibrium profile if 1 < x < 2. In this equilibrium, who if anyone, does the job? Explain your answer.

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