Question

Find the rationalizable strategies in the following game (Detailed problem-solving process)

504 A3. 33-2 ABC

Answer 1

1/2	A	B	C
A	3,5	2,5	1,2
B	3,2	0,0	0,1
C	2,0	1,4	5,2

For player 1 strategy B is weakly dominated by A because among A and B 3=3, 2>0 and 1>0. Therefore for player 1, A is dominating strategy than B. So as a rational player player 1 will never play B. So A is rational strategy for player 1. Now we eliminate strategy B from player-1's strategy space. If we remove strategy B from player-1's matrix payoff then we get the following payoff matrix.

1/2	A	B	C
A	3,5	2,5	1,2
C	2,0	1,4	5,2

Now from player 2's point of view strategy C is strictly dominated by strategy B. So player 1 can think that as a rational player 2 will not play strategy C. So here strategy B is rational strategy for player 2 given this payoff matrix. Now if player 1 remove strategy C from payoff matrix then we can get the following payoff matrix.

1/2	A	B
A	3,5	2,5
C	2,0	1,4

From here we can say for player 1 strategy C is strictly dominated by strategy A because 3>2, 2>1. So for player 1 A is dominating than C. So for player 1, A is rational strategy. From player 2's point of view player 2 can remove strategy C from player 1's strategy matrix. So strategy A is rational for player 1. Now after removing strategy C the payoff matrix becomes like following.

1/2	A	B
A	3,5	2,5

In the above payoff matrix the there is no rational strategy for player 2 because for both strategy A and B we have the value 5.

So rationalizable strategies for player 1 are strategy A for player 1 and strategy B for player 2.