# 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 This solution is **FREE** courtesy of BrainMass!

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 $200

b) To solve the game, isolate one strategy for one player and circle the other player's best outcome. For example, when Ben chooses X, Diane's best outcome is $1000 from choosing strategy X.

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 $200

A player has a dominant strategy if both of the player's outcomes from a single strategy are circled. That is not the case here, so neither player has a dominant strategy.

c) A Nash equilibrium exists in any cell in which both players' outcomes are circled. In this game, the two Nash equilibria are in the top left and bottom right corners.

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