Question

Assume that one firm will always locate at the top of the circle, and call that...

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.
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Answer #1

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