Question

Alice and Barbara are playing a one-stage guessing game. Each must choose a number between 1 and 4 (inclusive). Alice’s target is to match Barbara’s number. Barbara’s target is to name twice Alice’s number. Each receives $10 minus a dollar penalty that is equal to the absolute difference between her guess and her target. Solve this game by iteratively deleting dominating strategies. What will Alice and Barbara choose?

Answer 1

Alice has to choose what Barbara has said

While Barbara has to choose twice of what Alice has said .

Assumption :-

The compensation paid cannot exceed $10 :-

Let us assume both Alice and Barbara have chose 2 .

Now Alice will receive $10

But twice of Alice was 4 , however Barbara chose 2 Thus she will receive 10-(4-2) . $8

The compensation paid can exceed $10 :-

Let us again take the above example , Now Payment will be equal to $10- (guess - target )

So Barbara will receive $10 - (2-4) = 10-(-2)=12

However to form the matrix we have ignored the second case and assumed that compensation cannot exceed $10 .( This is only an assumption because , it is not clearly mentioned in the question which method to use )