Question

Your company's new portable phone/music player/PDA/bottle washer, the RunMan, will compete against the established market leader, the iNod, in a saturated market. (Thus, for each device you sell, one fewer iNod is sold.) You are planning to launch the RunMan with a traveling road show, concentrating on two cities, New York and Boston. The makers of the iNod will do the same to try to maintain their sales. If, on a given day, you both go to New York, you will lose 900 units in sales to the iNod. If you both go to Boston, you will lose 650 units in sales. On the other hand, if you go to New York and your competitor to Boston, you will gain 1,600 units in sales from them. If you go to Boston and they to New York, you will gain 600 units in sales. What fraction of time should you spend in New York and what fraction in Boston?

You should spend  of your time in New York and  in Boston.

How do you expect your sales to be affected?

Answer 1

2 cities that need to be covered = Newyork and Botson

The probabilit of you going to Newyork = 1/2

The probability of you going to Boston = 1/2

Similarly probability of iNod going to Newyork and Batson is 1/2 and 1/2

When you are in Newyork, there are 2 possibilities regarding INOD: They are in newyork or they are in boston.

The probability that you are in newyork and inod is also in newyork = 1/2*1/2=1/4

The probability that you are in newyork and inod in boston = 1/2*1/2=1/4

If the bot players are in newyork, the loss in sales is (900/4)=225 units (loss)

If you are in newyork and inod in boston you again 1600 units gain.

=(1600/4)

=400 gain

The time that you spend in newyork results in net gain of 400-225=175(gain-losses)

If both companies are in boston, then loss in sales=(650/4) = 162.5

If you are in boston and inod in newyork gain in sales = 600/4=150

Net loss from being in boston=150-162.5=-12.5

Loss=-12.5

Therefore, The expected outcome is a net loss of run man sales.