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 3b 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. (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.
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 3b 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. (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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 3b 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.
(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.
(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.
(iv) Prove that for Damian, his choice of a = 1 strictly dominates his choice of a = 2
provided K< 144.
Transcribed Image Text: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)
=
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