My Math Forum Elements of game theory

 Probability and Statistics Basic Probability and Statistics Math Forum

 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
Math Team

Joined: May 2013
From: The Astral plane

Posts: 2,266
Thanks: 934

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
 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

 Tags elements, game, theory

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post DesertFox Probability and Statistics 9 August 5th, 2017 02:49 PM KoalaWithHat Applied Math 3 September 16th, 2013 12:57 PM musicgold Economics 0 March 14th, 2012 08:04 PM lkzavr Economics 1 April 22nd, 2009 11:35 AM lkzavr Applied Math 1 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top