<p>Consider the Bertrand’s Duopoly game with demand D(p) = α − p. Assume that each firm is restricted to choose a price is an integer. Also, assume that each firm has a constant marginal cost c is an integer and that α &gt; c+10.                                           (a) Show that (c+1,c+1) is not a nash equilibrium for the game.<br />
(b) Show that (c+2, c+2) is a nash equilibrium.</p>

CC BY-SA 4.0
2024-03-05T21:09:06.183Z
Hey, this sounds like it was an exercise meant to hone your skills, not mine! Maybe you should do it? If you get stuck and can explain where you get stuck, you can do so by editing your question.
Giskard
CC BY-SA 4.0
2024-03-06T06:25:37.060Z
The question is wrong . Are you sure you haven't reversed (a) and (b)? Pricing at c+1 is a NE, whereas pricing at c+2 isn't.
smcc
<nash-equilibrium><game-theory>
Bertrand Duopoly game
SHYAM
# Bertrand Duopoly game

(Asked by: username_0 on 2024-03-05)

Consider the Bertrand’s Duopoly game with demand D(p) = α − p. Assume that each firm is restricted to choose a price is an integer. Also, assume that each firm has a constant marginal cost c is an integer and that α > c+10. (a) Show that (c+1,c+1) is not a nash equilibrium for the game.  
(b) Show that (c+2, c+2) is a nash equilibrium.

**Tags:** nash-equilibrium, game-theory
> **Comments:**
> **username_1**: Hey, this sounds like it was an exercise meant to hone your skills, not mine! Maybe you should do it? If you get stuck and can explain where you get stuck, you can do so by editing your question.  
> **username_2**: The question is wrong . Are you sure you haven't reversed (a) and (b)? Pricing at c+1 is a NE, whereas pricing at c+2 isn't.  

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