Imagine that firm X chooses their quantity first, then firm Y observes the quantity of firm X and chooses their own quantity.  What is the subgame perfect Nash Equilibrium?  Is there a first or second-mover advantage here? You don't need to draw the whole game tree but you should give some kind of explanation for how you came to this equilibrium.

Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter15: Strategic Games
Section: Chapter Questions
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Imagine that firm X chooses their quantity first, then firm Y observes the quantity of firm X and chooses their own quantity.  What is the subgame perfect Nash Equilibrium?  Is there a first or second-mover advantage here? You don't need to draw the whole game tree but you should give some kind of explanation for how you came to this equilibrium. 

(You may assume that firm X can only choose quantities that are multiples of 200.  This prevents you from having to deal with prices that are not on the schedule and makes firm Y's strategy easier to write. )

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