In a game involving two players, if they reach a Nash equilibrium where neither player can improve their payoff by unilaterally changing their strategy, what can be said about the strategy profile if it is also subgame perfect?

In game theory, when we say that a strategy profile is a Nash equilibrium, it means that each player has chosen a strategy, and no one can do better by changing their strategy alone. If this equilibrium is also subgame perfect, it means that not only is it stable at the overall game level, but it is also stable at every possible point in the game. This means that even if the players are in the middle of the game and have to make decisions at different stages, they will still stick to their strategies because they have no incentive to change. For example, imagine two players deciding whether to cooperate or compete in a game. If they reach a Nash equilibrium where both decide to cooperate and this decision is also subgame perfect, then at any point in the game, if they were to revisit their choices, they would still choose to cooperate because it remains the best option for both.