There is small restaurant operating in the town of Farmingville. The small restaurant currently makes $5,000 in profit and sells only dishes using the local corn. There is a larger restaurant that currently makes $5,000 in profit operating in a nearby city, and also uses only the Farmingville corn.
The larger restaurant is considering opening a new location in Farmingville. If the larger restaurant does open in Farmingville it will make a total profit of $10,000. However, the smaller restaurant will have its profits reduced to $2,000. If the larger restaurant does open in Farmingville the smaller restaurant can choose to shutdown the local corn production leaving both restaurants with $0 in total profit.
a. Represent the game in extensive form.
b. What is the subgame perfect Nash equilibrium?