Consider the Bertrand Game with homogeneous firms. The game which is identical to that one except...
Consider the Bertrand Game with homogeneous firms. The game which is identical to that one except that now there are three firms. Recall that the marginal cost per unit produced is 10. Select ALL correct statements.
A: There exists a unique Nash equilibrium (10, 10, 10).
B:(10, 12, 9) is a Nash equilibrium.
C:(10, 10, 11) is a Nash equilibrium.
D:(10, 11, 12) is a Nash equilibrium.
E: There are infinitely many Nash equilibria.
F:(10, 10, 6) is a Nash equilibrium.
Homework Answers
In Bertrand equilibrium, no firm will be able to sell the product if it charges a higher price than the others. So, option B, C, D and F can be eliminated.
No firm will charge less than $10 as it will be more profitable to shut down in that case.
If each firm charges, more than $10, equilibrium will be unstable as each firm will have an incentive to cheat.
So, there can be unique Nash equilibrium (10,10,10)
Correct option is
A: There exists a unique Nash equilibrium (10, 10, 10).
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