Every Nash equilibrium is Subgame perfect Nash equilibrium.

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Every Nash equilibrium is Subgame perfect Nash equilibrium.

This statement is wrong. I show this by an counter example.

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Is this example enough and good to disprove this statements?

Please share your ideas with me.

Thank you

Note: in the paper, there is typo.

(Out, price war) is not SPNE, but NE. (In, accomodate) is NE and SPNE. So, NE set covers all SPNE. But, SPNE set doesnt cover all NE