Column L M R Row T B 1 What are the Row Players dominated st

Column: L, M, R

Row: T, B

1. What are the Row Players dominated strategies?

2. What are the Column Players dominated Strategies?

3. Which strategy will the column or row player never play? (Cross that out)

4. With the left over strategies, what is the row players dominated startegy?

5. With the left over startegies, what are the column players dominated strategy?

6. Which strategy will the Column or row player never play? (Cross that out?)

7. With the left over startegies, what is the row players dominated startegy?

8. With the left over strategies, what is the column players dominated strategy?

9. Which strategy will the column or row player never play? (Cross that out)

10. What is the equilibrium?

Solution

Payoff Matrix will be written as

L M R

T (3,4) (4,3) (2,2)

B (4,1) (2,0) (3,4)

Ans 1)

Row player has 2 strategies in total (T,B) but none of the strategy dominates other because for T and B (3<4,4>2 & 2,3) hence Row player has no dominnated strategy

Ans 2)

For Column player we have strategy L dominating strategy over M because for L & M (4>3,1>0) therefore M is dominated by L for Column player

Ans 3)

Column and Row player will never play strategy (T,M) & (B,M)

Ans 4)

After removine dominated strategy from payoff we get reduced payoff matrix of 2*2 form

L R

T (3,4) (2,2)

B (4,1) (3,4)

Now Row layer has dominating strategy B over T because (4>3,3>2)

Hence dominated strategy for Row player is T\\

Ans 5)

Now if we again cross the strategy which is dominated then we left with 1 row and 2 columns

Hence Nash Equilibrium is strategy (B,R)=(3,4)