<p>If the question is whether not taking the covid vaccine is free-riding, then the answer is NO. In a Prisoner's Dilemma or a Public Good Game in the standard sense, free-riding (defection) is by definition a strictly dominant strategy. If this were true for not taking the vaccine, that would mean it is strictly better not to take the vaccine even if nobody else is vaccinated. This is obviously wrong.</p>
<p>In a more realistic model you would work with a large population. Vaccination prevents illness but comes at a small cost. The probability of infection depends on the vaccination rate in the population. If the vaccination rate reaches the level required for herd immunity, this probability is zero even for the unvaccinated. It can then be shown that <a href="https://www.pnas.org/content/101/36/13391" rel="noreferrer">in equilibrium herd immunity will not be reached</a>. However, even though <a href="https://www.science.org/doi/10.1126/science.287.5453.601" rel="noreferrer">Robert May likened this problem to a Prisoner's Dilemma</a>, the game is rather a variant of the Volunteer's Dilemma, not a Prisoner's Dilemma or a Public Good Game.</p>

CC BY-SA 4.0
2022-02-04T13:18:14.137Z
Well, thank you. I think I am getting your point. The more it surprises me that the professor suggests to apply a public good game approach to model the scenario.
Diana
CC BY-SA 4.0
2022-02-04T12:40:29.373Z
2022-02-04T12:40:29.373Z
VARulle
<p>I am a student and completely new to Game Theory, in fact, it is an additional course for me, I am actually from an entirely different field. I am asked to choose a Game Theory approach to model the question whether not taking the vaccine is free riding. All I know is that it would make sense to make use of a public good game theory model such as the prisoner's Dilemma, but I do not know how to analyze it, whether there are nash equilibria and what that would mean, and how political measurements could positively influence the whole scenario. Anyone willing to help me with some explanations? There should not be more than 2 players. Thanks in advance.</p>

CC BY-SA 4.0
2022-02-04T10:57:48.983Z
Being vaccinated has a public benefit, but it also has very clearly a private benefit. This is very different from the prisoner's dilemma. Not too long ago, people complained about people using their power to get early access to vaccines.
Michael Greinecker
CC BY-SA 4.0
2022-02-04T11:11:14.640Z
So would you suggest a different model?
Diana
CC BY-SA 4.0
2022-02-04T11:22:31.657Z
I think your instructor asked you something unreasonable to do. I don't see how one can learn much from a two-player game-theoretic model here.
Michael Greinecker
CC BY-SA 4.0
2022-02-04T11:23:11.493Z
You must also consider the marginal public benefit of a person taking vaccine in addition to wear mask.
High GPA
CC BY-SA 4.0
2022-02-04T11:28:07.977Z
He said I should answer the question using Public Good Game Theory approaches. I don't know about this 2 player thing, but it's an introductory course, max 2 or 3 player examples are given on the slides. Can anyone suggest something? My head is burning
Diana
<game-theory><nash-equilibrium>
Game Theory Model needed to model the question whether "not taking the covid vaccine is free-riding"
Diana
# Game Theory Model needed to model the question whether "not taking the covid vaccine is free-riding"

(Asked by: username_0 on 2022-02-04)

I am a student and completely new to Game Theory, in fact, it is an additional course for me, I am actually from an entirely different field. I am asked to choose a Game Theory approach to model the question whether not taking the vaccine is free riding. All I know is that it would make sense to make use of a public good game theory model such as the prisoner's Dilemma, but I do not know how to analyze it, whether there are nash equilibria and what that would mean, and how political measurements could positively influence the whole scenario. Anyone willing to help me with some explanations? There should not be more than 2 players. Thanks in advance.

**Tags:** game-theory, nash-equilibrium

> **Comments:**
> **username_1**: Being vaccinated has a public benefit, but it also has very clearly a private benefit. This is very different from the prisoner's dilemma. Not too long ago, people complained about people using their power to get early access to vaccines.  
> **username_0**: So would you suggest a different model?  
> **username_1**: I think your instructor asked you something unreasonable to do. I don't see how one can learn much from a two-player game-theoretic model here.  
> **username_2**: You must also consider the marginal public benefit of a person taking vaccine in addition to wear mask.  
> **username_0**: He said I should answer the question using Public Good Game Theory approaches. I don't know about this 2 player thing, but it's an introductory course, max 2 or 3 player examples are given on the slides. Can anyone suggest something? My head is burning  

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## 1 answers

### Answer by username_3 on 2022-02-04. Score: 5

If the question is whether not taking the covid vaccine is free-riding, then the answer is NO. In a Prisoner's Dilemma or a Public Good Game in the standard sense, free-riding (defection) is by definition a strictly dominant strategy. If this were true for not taking the vaccine, that would mean it is strictly better not to take the vaccine even if nobody else is vaccinated. This is obviously wrong.

In a more realistic model you would work with a large population. Vaccination prevents illness but comes at a small cost. The probability of infection depends on the vaccination rate in the population. If the vaccination rate reaches the level required for herd immunity, this probability is zero even for the unvaccinated. It can then be shown that [in equilibrium herd immunity will not be reached](https://www.pnas.org/content/101/36/13391). However, even though [Robert May likened this problem to a Prisoner's Dilemma](https://www.science.org/doi/10.1126/science.287.5453.601), the game is rather a variant of the Volunteer's Dilemma, not a Prisoner's Dilemma or a Public Good Game.

> **Comments:**
> **username_0**: Well, thank you. I think I am getting your point. The more it surprises me that the professor suggests to apply a public good game approach to model the scenario.  

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