# Construct a game with only pure strategy nash equilibrium [closed]

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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## closed as off-topic by denesp, HRSE, optimal control, FooBar, cc7768Feb 15 at 16:32

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