You and your rival must simultaneously decide what price to advertise in the wee

Question

You and your rival must simultaneously decide what price to advertise in the weekly newspaper. If you each charge a low price, you each earn zero profits. If you each charge a high price, you each earn profits of $3. If you charge different prices, the one charging the higher price loses $5 and the one charging the lower price makes $5.


a. Find the equilibrium when there are no repeated transactions.







b. Now, suppose there are repeated transactions. If the interest rate is 10%, what will be the outcome?
(Note: there is no need to work out net present value; it is just mentioned to make the exercise realistic.)

Explanation / Answer

first let us set up a matrix

                      rival

                           low    high

you         low       0,0      5,-5

              high       -5,5    3,3

We can now compare payoffs

A. nash equilibrium is you and rival to price low (low,low)

B.

In this case, we know what our rival moves so we can anticipate what they do. Therefore we can predict NE to be (low,high) We can do so because we anticipate rivals move

Hope this helps

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