# Nash equilibrium and dominant strategies

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 pick B, they get $100 each. If player 1 picks A, and player 2 picks B then player 1 gets $0 and player 2 gets $650. If player 1 chooses strategy B, and player 2 picks strategy A, then player 1 gets $650 and player 2 gets $0.

a) Write the above game in normal form.

b) Find each player's dominant strategy, if it exists.

c) Find the Nash equilibrium (or equilibrium) of this game.

d) Rank strategy pairs by aggregate payoff (highest to lowest)

e) Can the outcome with the highest aggregate payoff be sustained in equilibrium? Why or why not.

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#### Solution Preview

To put the game in normal form, we create a matrix showing each player's moves. Player 1's payoffs are on the left of each pairing.

Player 1

A ...

#### Solution Summary

Nash equilibrium, aggregate payoff and dominant strategies