= Damian and Kira trade in antique cars. They typically buy either 1 or 2 cars at any given time, since they are difficu

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Damian And Kira Trade In Antique Cars They Typically Buy Either 1 Or 2 Cars At Any Given Time Since They Are Difficu 1 (343.72 KiB) Viewed 28 times

= 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 Q is the total number of cars traded at a given time, is determined by the demand equation: K P(Q) Q2' where K is a positive constant. If a € {1,2} is Damian's choice and b € {1,2} is Kira's choice, (so Q = (a + b)) it costs Damian 2a to find and prepare a cars for market, and it costs Kira 36 to get b cars ready for market. Damian has better connections and access the cars before Kira, and so Damian chooses his 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 difference between how much they can sell their cars for, minus the total costs to prepare them for sale. (i) Express this game as an extensive form game tree, making sure to fully label all the nodes and links, and especially writing down their payoffs. [7 marks] (ii) Using the specific choice of K 144, convert the game tree into an extended strategic form game matrix, and find the Nash equilibria, and the unique subgame perfect equilibrium in pure strategies. [6 marks] (iii) Explain the difference between the Nash equilibria found from the strategic form game matrix and the unique subgame perfect equilibrium, which one is more appro- priate to use and why. [5 marks] (iv) Prove that for Damian, his choice of a = 1 strictly dominates his choice of a 2 provided K < 144. [7 marks]