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the first thing you want to do is what?
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You want to look at the sub-game.
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You want to look at what would happen if you did invest
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and solve out the new Nash equilibrium in that sub-game.
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Then you want to roll back the value of that sub-game
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back into the initial decision which is the strategic investment decision
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whether to rent this machine or not.
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So schematically, the game looks like this: rent or not rent,
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and in either case you play Cournot.
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There's a sub-game in each case.
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In this case you play symmetric Cournot,
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when you both have the same costs;