One-Shot Nash equilibrium is (A, C).
Yes the players can achieve payoffs that are better than the one-shot Nash equilibrium.
This is due to the fact that player 2 will choose strategy C if player A chooses option A. Player 2 will immediately choose Plan C if Player A chooses Option B. As a result, C becomes the second player's dominant strategy. The optimal decision for player 1 is to choose strategy A if player 2 chooses option C. Player 1 will select A if Player 2 chooses to choose D, making this Player 1's dominant move.
A Nash equilibrium is necessary for matrix reward games with two players if the row chosen is to maximize the payoff for the row player given the column chosen by the column player, and the column, in turn, is to maximize the payoff for the column player given the row chosen by the row player.
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