Example of Iterated Deletion of Dominated Strategies

Example of an iterated deletion of dominated strategy equilibrium

Consider the following game to better understand the concept of iterated elimination of strictly dominated strategies.

Player 1 has two strategies and player 2 has three. S1={up,down} and S2={left,middle,right}. For player 1, neither up nor down is strictly dominated. Up is better than down if 2 plays left (since 1>0), but down is better than up if 2 plays right (since 2>0). For player 2, however, right is strictly dominated by middle (since 2>1 and 1>0), so player 2 being rational will not play right.

Thus if player 1 knows that player 2 is rational then player 1 can eliminate right from player 2's strategy space. So, if player 1 knows that player 2 is rational then player 1 can play the game as if it was the game depicted below.

In the figure above, down is strictly dominated by up for player 1 , and so if player 1 is rational (and player 1 knows that player 2 is rational, so that the second game applies) then player 1 will not play down. Consequently, if player 2 knows that player 1 is rational, and player 2 knows that player 1 knows that player 2 is rational ( so that player 2 knows that the second game applies) then player 2 can eliminate down from player 1's strategy space, leaving the game looking like below.

And now left is strictly dominated by middle for player 2 , leaving (up,middle) as the outcome of the game. This is process is called the iterated elimination of strictly dominated strategies.