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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

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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.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!