# Game Theory: Finding Dominant Strategy and Nash Equilibrium

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.

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.