<p>Pure strategy Nash equilibria are a subset of mixed strategy Nash equilibria, so as long as your statement </p>

<blockquote>
  <p>a mixed strategy Nash equilibrium always exists and all such equilibria have the same value</p>
</blockquote>

<p>is true, all pure strategy Nash equilibria will have the same value as well.</p>

CC BY-SA 4.0
2020-06-09T07:32:11.820Z
It seems that I was asking a dumb question =_=
Mengfan Ma
CC BY-SA 4.0
2020-06-09T07:23:58.230Z
2020-06-09T07:23:58.230Z
Giskard
<p>Given a two-person zero-sum game, a mixed strategy Nash equilibrium always exists and all such equilibria have the same value. A pure strategy Nash equilibrium, however, may not exist.</p>

<p>My question is: suppose that a pure strategy Nash equilibrium exists, does the value of it equal the value of the mixed strategy Nash equilibrium?</p>

<game-theory><nash-equilibrium>
Does the value of a pure strategy Nash equilibrium(if exists) equal the value of the mix strategy Nash equilibrium in two-person zero-sum game?
Mengfan Ma
# Does the value of a pure strategy Nash equilibrium(if exists) equal the value of the mix strategy Nash equilibrium in two-person zero-sum game?

(Asked by: username_0 on 2020-06-09)

Given a two-person zero-sum game, a mixed strategy Nash equilibrium always exists and all such equilibria have the same value. A pure strategy Nash equilibrium, however, may not exist.

My question is: suppose that a pure strategy Nash equilibrium exists, does the value of it equal the value of the mixed strategy Nash equilibrium?

**Tags:** game-theory, nash-equilibrium


---

## 1 answers

### Answer by username_1 on 2020-06-09. Score: 4 | Accepted answer

Pure strategy Nash equilibria are a subset of mixed strategy Nash equilibria, so as long as your statement

> a mixed strategy Nash equilibrium always exists and all such equilibria have the same value

is true, all pure strategy Nash equilibria will have the same value as well.

> **Comments:**
> **username_0**: It seems that I was asking a dumb question =_=  

---

