Business person A has the option of taking out a bank-loan for opening a store that would compete with business person B, who already owns a store. Business personB, not knowing whether or not A has taken out a loan, can decide whether or notwhether or not to drop his prices. Person A then observes whether or not B has dropped his prices and, if he previously elected to take out a bank loan, may decide whether or not to open a competing store (matching B's prices).
Here is what we know about both A and B's utility in this scenario:
- Not taking out a loan = 0- Taking out a loan = -2
- Owning a store with high prices and no competitor: +5
- Owning a store with low prices and no competitor: +3
- Owning a store with high prices and a competitor: +3
- Owning a store with low prices and a competitor: +1
Diagram this interaction as a game in extensive form. Solve for the sub-perfectequilibria. Solve for the Nash equilibria.