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Game Theory: Finding Dominant Strategy and Nash Equilibrium

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Please help with the following problem.

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.

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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.

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 ...

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