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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.

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  • $\begingroup$ This discussion on when games can have an even number of equilibria will probably help: mindyourdecisions.com/blog/2014/10/07/… $\endgroup$ – Giskard Feb 11 '16 at 12:39
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    $\begingroup$ I'm voting to close this question as off-topic because it has been cross posted on math.stackexchange. $\endgroup$ – Giskard Feb 11 '16 at 22:29
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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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