Question

Two competing firms are choosing where to locate new stores. First, Firm 1 decides whether to locate in Downtown (D) or Uptown (U). After Firm 2 sees the decision Firm 1 made, Firm 2 chooses Downtown or Uptown. Uptown is a more profitable location than Downtown; a firm choosing Uptown earns a profit of $700,000 if the other firm also chose Uptown, or $1,300,000 if the other firm chose Downtown, while a firm choosing Downtown earns $400,000 if the other firm also chose Downtown, or $900,000 if the other firm chose Uptown.

a. Draw a game tree below to represent this situation. (5p)
b. Find the Nash equilibrium of this game. (5p)
Please let it be clear.

Answer 1

a. Here is the game tree representing the situation:
```
Firm 1
/ \
/ \
Downtown Uptown
/ \ / \
/ \ / \
Downtown Uptown Downtown Uptown
```

b. The Nash equilibrium of this game is for both firms to locate in Uptown. If Firm 1 locates in Downtown, Firm 2 has an incentive to locate in Uptown, since it earns a higher profit of $1,300,000. Similarly, if Firm 1 locates in Uptown, Firm 2 has an incentive to locate in Uptown, since it earns a higher profit of $700,000. Therefore, the only stable outcome is for both firms to locate in Uptown, where they both earn a profit of $700,000.