Question

4. Consider the following game matrix: LCR T 3 ,1 0,0 4,1 M10, 02, 24, 3 B 7,6 | 1,2 3,1 (a) Find all the strictly dominated (pure) strategies for each player. (b) Find all the weakly dominated (pure) strategies of each player. (c) Does the game has a strict dominant strategy equilibrium?

Answer 1

player 2 T31 0,0 OD player 1 M100 2203 B 7,6 1,2 3,1

A) strictly dominated strategies:
Player 1- B
Player 2 - C

B) weakly dominated strategies:
Player 1- T
Player 2- none.

Explanation:
a) for player 1: strategies are- T,M,B

When player 2 chooses L, player 1 will choose M because 10>3and 7.
When player 2 chooses C, player 1 will choose M because 2> 0 and 1.
When player 2 chooses R, player 1 will choose either T or M because 4 > 3.
Because the strategy B is never chosen, it is STRICTLY DOMINATED strategy of player 1.

Also, for player 1, because the strategy M is better than or as good as strategy T , M weakly dominates strategy T.
Hence, strategy T is WEAKLY DOMINATED STRATEGY of player 1.

For player 2: Strategies are- L,C,R.

When player 1 chooses T,
Player 2 chooses L or R because 1>0.
When player 1 chooses M,
Player 2 chooses R because 3> 0 and 2.
When player 1 chooses B,
Player 2 chooses L because 6>2 and 1.

Hence, player 2 never chooses C so C is STRICTLY DOMINATED STRATEGY for player 2.

Because no same strategy is as good as or better than the other strategy , player 2 has no weakly dominated strategy.

C) because player 2 has no dominant strategy , there are no strictly dominant strategy Nash equilibrium.