Assume that one firm will always locate at the top of the circle, and call that 0°. Then we know, for example, that with three firms, one Nash equilibrium has the firms locating at 0°, 120°, and 240°; and that the “most extreme” Nash equilibrium has the firms locating at (for example) 0°, 90°, and 180°. Here, “most extreme” means “as far as possible from perfect rotational symmetry”; you could also interpret it as “having the largest possible gap between some two firms”.

Suppose that entry costs $40.

1. Is there a Nash equilibrium with 3 firms entering? Explain.
   [Note: think about both whether a new firm could profitably enter, and whether existing firms are profitable and want to stay in the market.]
2. Is there a Nash equilibrium with 4 firms entering? Explain.
3. Is there a Nash equilibrium with 5 firms entering? Explain.
4. What is the largest number of firms that could constitute a Nash equilibrium in this game? Explain.