Homework Answers
Solution:
We can solve for the Nash equilibrium in this sequential game using backward induction. In case of backward induction, we solve from end (the last mover player that is HC).
So, assuming that LD played DIY, HC's best response would be to play WDI (as 400 > 150). Similarly, had LD played WDI, HC's best response would have been to play DIY, as 120 > 50.
Knowing what HC would choose, after LD makes a choice, LD will compare the following two alternatives:
LD playing DIY, HC playing WDI, generating payoff vector of (150, 400), while LD playing WDI, HC playing DIY, generating payoff vector of (300, 120). As 300 > 150, LD gets a higher payoff by playing WDI.
Thus, the Nash equilibrium is (LD, HC) = (WDI, DIY) = (300, 120).
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