<p>In a somewhat degenerate way, yes. The specified demand function is a trivial case of a best response function describing the optimal quantity demanded for any given price of the monopolist. The monopolist's optimal profit-maximizing price in turn is the best response facing this demand. So you end up with a Nash equilibrium, where each player plays his/her best response and the choices are mutually consistent. Put differently, no player has any incentive to deviate.</p>

CC BY-SA 4.0
2022-03-02T21:10:32.543Z
Relatedly, one can have also a competitive market where the monopolist price is a Nash equilibrium. See the Diamond paradox from industrial organization, where there are nonnegligible search costs to finding the best price.
JD Montgomery
CC BY-SA 4.0
2022-03-03T15:03:21.330Z
Why is this »degenerate« ... whatever that means in an economic context?
Jesper Hybel
CC BY-SA 4.0
2022-03-04T17:55:42.477Z
Because I would not consider this your typical case of the intersection of two fully-fledged best response functions.
jpfeifer
CC BY-SA 4.0
2022-03-02T12:35:56.213Z
2022-03-02T12:35:56.213Z
jpfeifer
<p>Consider a monopoly with price power in the market and the demand is a function of price. Can the result of such a monopoly problem be called a nash equilibrium?</p>

<nash-equilibrium><monopoly>
Is a Monopoly equilibrium also a Nash equilibrium?
DevinY
# Is a Monopoly equilibrium also a Nash equilibrium?

(Asked by: username_0 on 2022-03-02)

Consider a monopoly with price power in the market and the demand is a function of price. Can the result of such a monopoly problem be called a nash equilibrium?

**Tags:** nash-equilibrium, monopoly

---

## 1 answers

### Answer by username_1 on 2022-03-02. Score: 4

In a somewhat degenerate way, yes. The specified demand function is a trivial case of a best response function describing the optimal quantity demanded for any given price of the monopolist. The monopolist's optimal profit-maximizing price in turn is the best response facing this demand. So you end up with a Nash equilibrium, where each player plays his/her best response and the choices are mutually consistent. Put differently, no player has any incentive to deviate.

> **Comments:**
> **username_2**: Relatedly, one can have also a competitive market where the monopolist price is a Nash equilibrium. See the Diamond paradox from industrial organization, where there are nonnegligible search costs to finding the best price.  
> **username_3**: Why is this »degenerate« ... whatever that means in an economic context?  
> **username_1**: Because I would not consider this your typical case of the intersection of two fully-fledged best response functions.  

---

