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 May 22nd, 2019, 10:54 AM #1 Newbie   Joined: May 2019 From: Romania Posts: 3 Thanks: 0 Elements of game theory The federal government desires to inoculate its citizens against a certain flu virus. The virus has two strains, and the proportions in which the two strains occur in the virus population are not known. Two vaccines have been developed. Vaccine 1 is 85% effective against strain 1 and 70% effective against strain 2. Vaccine 2 is 60% effective against strain 1 and 90% effective against strain 2. What inoculation policy should the government adopt?
 May 22nd, 2019, 01:42 PM #2 Global Moderator   Joined: May 2007 Posts: 6,821 Thanks: 723 Use both?
May 22nd, 2019, 01:58 PM   #3
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 Originally Posted by levivike The federal government desires to inoculate its citizens against a certain flu virus. The virus has two strains, and the proportions in which the two strains occur in the virus population are not known. Two vaccines have been developed. Vaccine 1 is 85% effective against strain 1 and 70% effective against strain 2. Vaccine 2 is 60% effective against strain 1 and 90% effective against strain 2. What inoculation policy should the government adopt?
I know nothing of Game Theory, but this sounds like a minimization problem in Calculus or a linear programming in Linear Algebra.

Either way we have the equations:
$\displaystyle V_1 = (1 - 0.85) s_1 + (1 - 0.70) s_2$

$\displaystyle V_2 = (1 - 0.60) s_1 + (1 - 0.90) s_2$

Where we wish to minimize $\displaystyle s_1 + s_2$.

I need someone to check my logic here. Is this the correct setup?

-Dan

 May 22nd, 2019, 02:15 PM #4 Member     Joined: Oct 2018 From: USA Posts: 89 Thanks: 61 Math Focus: Algebraic Geometry I know nothing of Game Theory either but just as an intuition V1 : $(1-0.85)+(1-0.7) = 0.45$ V2: $(1-0.6)+(1-0.9) = 0.5$ Since $0.45 < 0.5$ vaccine 1 is more effective.....? Could be wrong but it seems reasonable. Thanks from topsquark

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