Damian and Kira trade in antique cars. They typically buy either 1 or 2 cars at any giventime, since they are difficult to find and expensive. The price per car P(Q) where Qisthe total number of cars traded at a given time, is determined by the demand equation:KP(Q) - 52²=where K is a positive constant. If a € {1, 2} is Damian's choice and b = {1, 2} is Kira'schoice, (so Q = (a + b)) it costs Damian 2a to find and prepare a cars for market, and itcosts Kira 3b to get b cars ready for market.Damian has better connections and access the cars before Kira, and so Damian chooseshis value of a first. Kira then chooses his value of b, knowing Damian's choice.Their choices are determined by maximising their individual profits, ie the differencebetween how much they can sell their cars for, minus the total costs to prepare them forsale.(i) Express this game as an extensive form game tree, making sure to fully label all thenodes and links, and especially writing down their payoffs.(ii) Using the specific choice of K = 144, convert the game tree into an extendedstrategic form game matrix, and find the Nash equilibria, and the unique subgameperfect equilibrium in pure strategies.(iii) Explain the difference between the Nash equilibria found from the strategic formgame matrix and the unique subgame perfect equilibrium, which one is more appro-priate to use and why.(iv) Prove that for Damian, his choice of a = 1 strictly dominates his choice of a = 2provided K < 144.Purks

A Nash equilibrium occurs when no player can improve their payoff by switching to a different…

Damian and Kira trade in antique cars. They typically buy either 1 or 2 cars at any given time, since they are difficult to find and expensive. The price per car P(Q) where Qis the total number of cars traded at a given time, is determined by the demand equation:

Damian and Kira trade in antique cars. They typically buy either 1 or 2 cars at any given time, since they are difficult to find and expensive. The price per car P(Q) where Qis the total number of cars traded at a given time, is determined by the demand equation:

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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