decision theory April 2017 Q1(ii) CT6

[dan r]

Hi all

hope you are well

John enjoys playing two player zero-sum games.

The matrix below shows the losses to John in a particular two player zero-sum game. His strategies are denoted by I, II and III, whereas the strategies for his opponent are denoted by a, b and c.

I II III
a -3 2 4
b 0 1 -1
c 1 3 0

(i) Explain which of John’s strategies is dominated. [2]

The opponent now has the option of a fourth strategy, d, which results in none of John’s strategies being dominated.

(ii) Suggest possible values for the strategy

I am struggling to understand part 2 of question 1...

A further quick question would be around negative numbers. If he is trying to minimise his loss, would a value of -3 = gain of 3 in this example?

thank you

 

[John Lee]

So in part (i) we can see that I dominates II as every loss is lower.

For part (ii) all you need to do is ensure the value for I d is a bigger loss than II d. Then I will no longer dominate II.