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May 22nd, 2019, 10:54 AM   #1
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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?
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May 22nd, 2019, 01:42 PM   #2
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May 22nd, 2019, 01:58 PM   #3
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Quote:
Originally Posted by levivike View Post
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
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May 22nd, 2019, 02:15 PM   #4
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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.
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