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# Game Theory: two-player, one-shot simultaneous-move game

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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 \$500. If both players choose strategy, each earns a payoff of \$100. If player one chooses strategy A and player 2 chooses strategy B, then the player 1 earns \$0 and player 2 earns \$650. If player 1 chooses B and player 2 chooses strategy A, then player 1 earns \$650 and player 2 earns \$0.

a. Write the above game in normal form.
b. Find each player's dominant strategy, if it exists.
c. Find the Nash equilibrium of this game.
d. Rank strategy pairs by aggregate payoffs (highest to lowest).
e. Can the outcome with the highest aggregate payoff be sustained in equilibrium? Why or why not.

#### Solution Preview

a) The normal form of this game is as follows:
| Player 2 chooses strategy A | Player 2 chooses strategy B
------------------------------------------------------------------------------------------------------------
Player 1 chooses strategy A | \$500, \$500 | \$0, ...

#### Solution Summary

Gives the norm form, dominant strategy and Nash equilibrium for a described game.

\$2.49