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Should this offer fundamentally alter the outcome of the

Consider the situation the economics professor faces in Problem 6, but now let's suppose that Dave makes you the following offer: "Let's really soak this guy. I'll pass on turns 2 and 4 if you'll go halves on the 500 bucks with me." Should this offer fundamentally alter the outcome of the game? (Hint: Think about this problem using backward induction!)

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