Strictly Dominated Strategies and Proper Equilibrium Consider the 3-person game where player 1 chooses rows, player 2 chooses columns, and player 3 chooses matrices. (a) First assume that player 3 is...

Strictly Dominated Strategies and Proper Equilibrium

Consider the 3-person game

where player 1 chooses rows, player 2 chooses columns, and player 3 chooses matrices.

(a) First assume that player 3 is a dummy and has only one strategy, namely L. Compute the perfect and proper Nash equilibrium or equilibria of the game.

(b) Now suppose that player 3 has two pure strategies. Compute the perfect and proper Nash equilibrium or equilibria of the game. Conclude that adding a strictly dominated strategy (namely, R) has resulted in an additional proper equilibrium.