<p>This was cross-posted. See my answer to this question here:</p>

<p><a href="https://math.stackexchange.com/questions/1650075/construct-a-game-with-only-pure-strategy-nash-equilibrium">https://math.stackexchange.com/questions/1650075/construct-a-game-with-only-pure-strategy-nash-equilibrium</a></p>

CC BY-SA 3.0
2016-02-11T20:33:27.007Z
2016-02-11T20:33:27.007Z
2017-04-13T12:19:37.213Z
Rahul Savani
<p>I'm trying to construct a $4 \times4$ Normal-Form Game with two players, where each player has four strategies and it satisfies: </p>

<p>1) The game has exactly 4 Nash Equilibria</p>

<p>2) All equilibria involve only pure strategies (meaning there's no mixed strategy Nash Equilibrium)</p>

<p>Could someone give an example of this kind of game, and explain briefly how you construct it? I'm not sure when a game has no MSNE but only the PSNE. Thanks a lot.</p>

CC BY-SA 3.0
2016-02-11T12:39:13.603Z
This discussion on when games can have an even number of equilibria will probably help:
http://mindyourdecisions.com/blog/2014/10/07/game-theory-tuesdays-why-most-games-have-an-odd-number-of-nash-equilibria/
Giskard
CC BY-SA 3.0
2016-02-11T22:29:44.677Z
I'm voting to close this question as off-topic because it has been cross posted on math.stackexchange.
Giskard
<game-theory>
Construct a game with only pure strategy nash equilibrium
Emmav798
# Construct a game with only pure strategy nash equilibrium

(Asked by: username_0 on 2016-02-11)

I'm trying to construct a $4 \times4$ Normal-Form Game with two players, where each player has four strategies and it satisfies:

1) The game has exactly 4 Nash Equilibria

2) All equilibria involve only pure strategies (meaning there's no mixed strategy Nash Equilibrium)

Could someone give an example of this kind of game, and explain briefly how you construct it? I'm not sure when a game has no MSNE but only the PSNE. Thanks a lot.

**Tags:** game-theory
> **Comments:**
> **username_1**: This discussion on when games can have an even number of equilibria will probably help: http://mindyourdecisions.com/blog/2014/10/07/game-theory-tuesdays-why-most-games-have-an-odd-number-of-nash-equilibria/  
> **username_1**: I'm voting to close this question as off-topic because it has been cross posted on math.stackexchange.  

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## 1 answers

### Answer by username_2 on 2016-02-11. Score: 4

This was cross-posted. See my answer to this question here:

<https://math.stackexchange.com/questions/1650075/construct-a-game-with-only-pure-strategy-nash-equilibrium>


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