In a repeated game context, if two players consistently choose strategies that lead to a Nash Equilibrium, what is the most likely outcome over time?

In a repeated game context, when two players consistently choose strategies that lead to a Nash Equilibrium, they will likely continue to maintain that equilibrium over time. This happens because both players understand that if they change their strategy unilaterally, they would end up worse off, as the equilibrium is a stable state where neither player has an incentive to deviate. For example, imagine two friends deciding how to split a pizza; if they both agree on splitting it evenly and are happy with that, they will keep choosing that option in future orders. As they keep playing, their trust in each other grows, which reinforces their commitment to that strategy. Therefore, the most likely outcome is that they will keep sticking to the Nash Equilibrium, leading to stable and predictable results in their interactions.