Answer to Question #140482 in Microeconomics for Kris

Question

Your firm must decide whether or not to introduce a new product. If you introduce the
new product, your rival will have to decide whether or not to clone the new product. If
you don’t introduce the new product, you and your rival will earn $1 million each. If
you introduce the new product and your rival clones it, you will lose $5 million and
your rival will earn $20 million (you have spent a lot on research and development,
and your rival doesn’t have to make this investment to compete with its clone). If you
introduce the new product and your rival does not clone, you will make $100 million
and your rival will make $0.
a. Set up the extensive form (the decision tree and the outcomes) of this game.
b. Should you introduce the new product?
c. How would your answer change if your rival has “promised” not to clone your
product?
d. What would you do if patent law prevented your rival from cloning your product?

Answer 1

$$Solution$$

a)

b) We use the backward induction method to solve this problem.

Therefore, the rival gets to choose whether he wants to clone the new product or not. If he clones it he gets a pay-off of $20 million and $0 million if he does not clone. So he will choose to clone the new product as he gets a higher a pay-off.

Now given that the Rival chooses to clone it in case you introduce a new product, you would prefer to not introduce the product as it gives you a higher pay-off.

Hence, the Nash Equilibrium would be, Not Introduce a New Product. ($10, $10)

c) Yes, there is a subgame perfect equilibrium. The rival choosing to clone or not clone the product based on pay-off is the subgame. Here, the subgame perfect equilibrium is the rival choosing to clone the product and the equilibrium is (-$5, $20)

d) In the end, you will choose not to introduce the product and each gets a pay-off of $10 million.

Because if you have chosen to introduce the product and rival would clone the product you would have got -$5 million, but you are better off not introducing the product at all