Question

There are two strain of flu(F) virus and two types of vaccine. The first vaccine(V1), is 0.85 effective against F1 and 0.70 effective against F2, while the second vaccine(V2) is 0.60 effective against F1 and 0.90 against F2. The public health service is player 1 and nature is player 2. The service has to decide what percentage of vaccines manufactured and made available to the public are of V1 and V2. Determine how the public health service should proceed.

Answer 1

Answer on Question #37749, Math, Other

We have the game of two players: the public health care and the nature. So, the maxmin method can be used:

There are values of functions $v_{1}$ and $v_{2}$ in the table in order to values of $F: F_{1}$ or $F_{2}$ . Thus, we can find the maxmin value of $V_{i}(F)$ for all pairs $F$ (flue) and $V$ (vaccine):

$$\max _ {V} \min _ {F} V _ {i} (F _ {i}) = 0. 7;$$

Then we can find the argument $V_{i}$ for this value of $V = 0.7$ :

$$\arg \max _ {V} \left(\min _ {F} V _ {i} (F)\right) = V _ {1}.$$

So, the public health should proceed to make available vaccine V1.