In a two-player, one-shot simultaneous-move game each player can choose strategy
ID: 1208586 • Letter: I
Question
In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A each earns a payoff of $400. If both players choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy ? and player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100. Write the above game in normal form.. Find each player's dominant strategy, if it exists c. Find the Nash equilibrium of this game d. Which strategy pair has the highest aggregate payoff? Can the outcome with the highest aggregate payoff be sustained in equilibrium?Explanation / Answer
(a) Following is the complete table -
Player 2
Strategy
A
B
Player 1
A
$400, $400
$100, $600
B
$600, $100
$200, $200
(b) If Player 1 chooses strategy A then Player 2 will get $400 if he also chooses strategy A and will get $600 if he chooses strategy B. Since, pay-off is higher in case of strategy B; Player 2 will choose strategy B if Player 1 chooses strategy A.
If Player 1 chooses strategy B then Player 2 will get $100 if he chooses strategy A and will get $200 if he chooses strategy B. Since, pay-off is higher in case of strategy B; Player 2 will choose strategy B if Player 1 chooses strategy B.
As we can see that Player 2 is choosing strategy B irrespective of strategy chosen by Player 1. So, strategy B is the dominant strategy of Player 2.
If Player 2 chooses strategy A then Player 1 will get $400 if he also chooses strategy A and will get $600 if he chooses strategy B. Since, pay-off is higher in case of strategy B; Player 1 will choose strategy B if Player 2 chooses strategy A.
If Player 2 chooses strategy B then Player 1 will get $100 if he chooses strategy A and will get $200 if he chooses strategy B. Since, pay-off is higher in case of strategy B; Player 1 will choose strategy B if Player 2 chooses strategy B.
As we can see that Player 1 is choosing strategy B irrespective of strategy chosen by Player 2. So, strategy B is the dominant strategy of Player 1.
Thus,
Player 1's dominant strategy = Strategy B
Player 2's dominant strategy = Strategy B
(c) When both players have dominant strategies then combination of dominant strategies is the Nash equilibrium.
So, the Nash equilibrium of this game is (Strategy B, Strategy B).
(d) The strategy pair (Strategy A, Strategy A) has the highest aggregate pay-off.
(e) The outcome with the highest aggregate payoff cannot be sustained in equilibrium. This because both the players had dominant strategy (Strategy B) and they will be in sustained equilibrium when they are adopting their dominant strategy. In case, they adopt some other strategy then it would not be sustainable as sooner or later they will revert back to their dominant strategy.
Player 2
Strategy
A
B
Player 1
A
$400, $400
$100, $600
B
$600, $100
$200, $200
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