Question

An investor was considering stock purchase in two companies. He determined

the following payoff table contingent upon whether company A or B wins a competition for

share of the market.

State a1 (Investment in A) a2(Investment in B)

A wins 30 0

B wins 40 80

What is the Maximax and Maximin strategy? At what probability of A’s winning is the two value Strategies?  

Answer 1

$\def\arraystretch{1.5} \begin{array}{c:c:c} State& a_1 & a_2 \\ \hline A\ wins & 30 & 0 \\ \hline B \ wins & 40 & 80 \end{array}$

$\text{strategy }a_1\text{(Investment in A) is Maximin}$

$\text{the ability to get a minimum income of 30 for any outcome}$

$\text{strategy }a_2\text{(Investment in B) is Maximax}$

$\text{probability of earning 80 income with a favorable outcome}$

$\text{probability of A’s winning}$

$p*30+40*(1-p)=0*p+80*(1-p)$

$70p=40$

$p=\frac{4}{7}$

Answer:$a_1\text{ is Maximin};a_2\text{ is Maximin};p=\frac{4}{7}$