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Is every subgame perfect Nash equilibrium a Nash equilibrium? In perfect information games, every SPNE is the NE of its corresponding subgame, and that makes it an NE. But I think someone asked a similar question on this site and @Giskard and @VARulle replied with a counter-example. It was most likely the entry-deterrence model.

If anyone can help me with what might have been the original question and its possible counter-example, I would be able to read that up. It seemed interesting.

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    $\begingroup$ Is every game a subgame of itself? $\endgroup$ Oct 26, 2022 at 7:40
  • $\begingroup$ @MichaelGreinecker Yes. $\endgroup$
    – Rick_Morty
    Oct 26, 2022 at 8:00
  • $\begingroup$ Actually, with the other question we pointed out that that information is available in most textbooks. Could you let us know what you have read so far? $\endgroup$
    – Giskard
    Oct 26, 2022 at 9:06
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    $\begingroup$ Hint: The "NE" in "SPNE" stands for "NE". $\endgroup$
    – VARulle
    Oct 26, 2022 at 19:41
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    $\begingroup$ You have probably seen a comment of me to a question where someone said that he knows that not every NE is an SPNE, but he can't find an example for this. That's also odd, but somewhat different. An SPNE is by the most common definition a NE satisfying an additional condition, so your question is somewhat trivial. (The definition you cite doesn't state it that way, but together with the fact that a game is a subgame of itself it also establishes that an SPNE is a NE.) $\endgroup$
    – VARulle
    Oct 27, 2022 at 8:47

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