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(1) Is a Nash equilibrium from a simultaneous game expected to be the same subgame perfect Nash equilibrium in a sequential game? Is it always?

(1) Is a Nash equilibrium from a simultaneous game expected to be the same subgame perfect Nash equilibrium in a sequential game? Is it always? If it isn't always the case, why? (2) How does a dominant strategy affect a subgame perfect Nash equilibrium? Will a player with a dominant strategy always choose that in a sequential game? Why?

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