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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 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.