You woke up this morning to a troubling advertisement on TV: A+ Rental Cars' local competitor is

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Question:

You woke up this morning to a troubling advertisement on TV: A+ Rental Cars' local competitor is discounting their economy rentals. After doing a little digging, you discover that your competitor has launched an aggressive advertising campaign, reducing the price on their economy line from $32.99 to $24.99. Based on your knowledge of previous pricing practices, you expect a similar price reduction across all vehicle types. In your memo or short business report, include answers to the following questions:

How will A+ Rental Cars' weekly revenue be affected by the price cut if you maintain the revenue maximizing price that you specified previously? Hint: If you did not include Pcomp in your estimated demand curve, then perhaps you should revisit this decision.
Should A+ Rental Cars respond to the competition by reducing their price as well, or ignore the actions of the competitor and run the business as usual? If you decide that a price cut is preferred, how deep should the discount be? Can game theory be used to analyze this situation? Explain your reasoning and methodology thoroughly.
It would be labor intensive to re-analyze your situation every time your competitor changed their prices. Is there a way to develop a formula that would help you quickly pick a price in response to the price setting behavior of your competitor? Be as systematic as possible. A general, concise solution is ideal. Document the process you used to arrive at the "formula".
The corporate leadership team inquired about the use of a "price match guarantee". This policy would mean A+ Rental Cars will match our competitor's price for a certain vehicle category if their price is lower than ours. Please comment on the viability of the this policy. Is it a good idea? Why or Why not?
If the price match policy is a good idea, how widely should it be advertised? Explain.