If everyone has a dominant strategy in a simultaneous move game, then the action that is played by that strategy is played in all stages of any finitely repeated version of that game in any subgame perfect equilibrium.

Question

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If everyone has a dominant strategy in a simultaneous move game, it means that regardless of what the other players do, it is always the best option for a player to play that action. In a finitely repeated game, players have the opportunity to observe each other's actions in previous rounds and adjust their strategies accordingly. However, if there is a dominant strategy, there is no need for adjustment as it will always be the best option. Therefore, the dominant strategy will be played in all rounds of any subgame perfect equilibrium.

If Everyone Has a Dominant Strategy in a Simultaneous Move