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# Game Theory: Finding Dominant Strategy and Nash Equilibrium

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Two players, Ben and Diana, can choose strategy X or strategy Y. If both Ben and Diana choose strategy X, each earns a payoff of \$1000. If both players choose strategy Y, each earns a payoff of \$200. If Ben chooses strategy X and Diana chooses strategy Y, then Ben earns \$0 and Diana earns \$130. If Ben chooses strategy Y and Diana chooses strategy X, then Ben earns \$130 and Diana earns \$0.

a. Write the above game in matrix (normal) form.
b. Find each player's dominant strategy, if it exists.
c. Find the Nash equilibrium (or equilibria) of this game.

https://brainmass.com/economics/game-theory/game-theory-finding-dominant-strategy-nash-equilibrium-544449

#### Solution Preview

See the attached file.

a) The game in matrix form:
Diana chooses X Diana chooses Y
Ben chooses X Ben gets \$1000
Diana gets \$1000 Ben gets \$0
Diana gets \$130
Ben chooses Y Ben gets \$130
Diana gets \$0 Ben gets \$200
Diana gets ...

#### Solution Summary

This solution gives step-by-step instructions for how to:
a) Write a two-player game in matrix form.
b) Find each player's dominant strategy.
c) Find the Nash equilibrium of the game.

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