Skip to main content
The Actuary: The magazine of the Institute and Faculty of Actuaries - return to the homepage Logo of The Actuary website
  • Search
  • Visit The Actuary Magazine on Facebook
  • Visit The Actuary Magazine on LinkedIn
  • Visit @TheActuaryMag on Twitter
Visit the website of the Institute and Faculty of Actuaries Logo of the Institute and Faculty of Actuaries

Main navigation

  • News
  • Features
    • General Features
    • Interviews
    • Students
    • Opinion
  • Topics
  • Knowledge
    • Business Skills
    • Careers
    • Events
    • Predictions by The Actuary
    • Whitepapers
    • Moody's - Climate Risk Insurers series
    • Webinars
    • Podcasts
  • Jobs
  • IFoA
    • CEO Comment
    • IFoA News
    • People & Social News
    • President Comment
  • Archive
Quick links:
  • Home
  • The Actuary Issues
  • September 2021
General Features

The vaccine dilemma

Open-access content Wednesday 1st September 2021
Authors
Servaas Houben

Servaas Houben looks at the prisoner’s dilemma and how it can be applied to COVID-19 vaccination

web_p37_The-vaccine-dilemma_

Although the benefits of vaccination for a society are obvious, a non-negligible percentage of people are refusing this protection against COVID-19. In game theory, the ‘prisoner’s dilemma’ provides individual decision-makers with a similar problem: choosing an optimising strategy for individual players does not result in an optimal outcome for the whole of society. Game theory can also explain the current refusal of individuals to get vaccinated, and show the impact of incentives.

The prisoner’s dilemma

The prisoner’s dilemma is one of the most famous examples of game theory. In this game, two prisoners (Abi and Ben) are suspected of committing a crime. The prisoners can either remain silent or betray the other prisoner. The police do not have sufficient evidence to prosecute either of them on the principal charge without a betrayal from either prisoner, but there is sufficient evidence to convict them on a lesser charge. The prisoners are therefore offered an incentive in the form of a reduction in their sentence if they betray their partner. The two prisoners are not allowed to communicate.

Let’s suppose the payouts for the prisoners are as follows.

  • When neither betrays the other, there is a small penalty of -1 for the lesser charge

  • When there is sufficient proof (one betrays the other), there is a large penalty of -10 for the principal charge for the betrayed party, and the other is set free

  • If both of the prisoners confess, then each of them is penalised -9, because there is a small +1 reduction in the penalty for a confession.

szad

Looking at the payoff matrix in Table 1, we can see that the best option for both prisoners is to remain silent (top left). In this case, each of them receives a small penalty of -1 and the total negative benefit for the pair of them is -2. However, when looking at the optimising choice for each individual, it is always beneficial to choose betrayal:

  • Case 1: The other person stays silent – Choosing silence receives a penalty of -1, while choosing betrayal receives no penalty, so betrayal is the better option

  • Case 2: The other prisoner betrays – Silence leads to a penalty of -10, while betrayal receives only a penalty of -9, so betrayal is the better option.

Rational players will therefore choose their optimising strategy to betray, and the result will be the right bottom option, with a total negative benefit of -18 – worse than the total of -2 if they had both chosen to co-operate and stay silent.

“Current policies for providing positive incentives to vaccinated individuals will result in a better outcome for society as a whole”

COVID-19: The individual versus society

The example in the two-person game above can also be used for the choice of vaccination (V) or refusal (R). Instead of a game between two prisoners, it could be formulated as a game between an individual and wider society.

We assume the following payouts:

  • There is a small cost for receiving the vaccine of -1 (because some people suffer vaccination side effects and a small amount of pain)

  • Lockdown costs are severe at -10, and these occur when a large part of society refuses the  vaccine

  • The choice of a single individual cannot result in lockdown.

The game outcomes are summarised in Table 2. 

 

web_p39

The game is still the same from the individual perspective in the original prisoner’s dilemma: the better option for the individual is to refuse the vaccine, as this has the higher payout in each of the scenarios. In addition, the choice of a single individual does not have a material effect on society as a whole: no lockdown, evening curfew or school closure occurs because just one person decides not to take the vaccine. Therefore, the payouts to society will not be impacted by the choice of an individual; option V is best for society independently of the choice of the individual considered in this set-up.This shows that a single individual deciding not to get the vaccine does not negatively affect the payout to society, as the impact of the individual’s choice on the outcome of the game is immaterial. 

COVID-19: The group versus society

Now suppose that, instead of a single person, an entire substantial group – say, 50% of the population – refuses the vaccine. This alters the game, as a bigger group will have a material effect on the outcome for the rest of society. The game is now as in Table 3.

 web_p39_The-vacc                           

The group now has a material impact on society; if it decides to refuse the vaccine, this will affect the whole of society, implying there is a higher chance (50%) of lockdown.

This example agrees with the intuition that when a significant group decides not to get the vaccine, this does negatively affect the payout to society, as the impact of the groups’ choice on the outcome of the game is material.

The individual versus group paradox

This discussion shows that society can end up with a worse equilibrium (no one taking the vaccine) if the individual perception is that there is a penalty in receiving the vaccine and little cost while wider society is vaccinated. Clearly, one individual on their own does not impact the whole of society, so the optimising strategy for an individual person in Table 2 is not to take the vaccine. The individual on their own will not impact the possibility of lockdown, and by not taking the vaccine, they avoid the drawbacks of taking the vaccine, avoiding the small penalty of -1.

However, when a substantial part of society decides to play this strategy, the outcome of society as a whole worsens: as we can see in Table 3, when all of the individuals in a group decide not to receive the vaccine (based on their individual preference in Table 2), the best possible response from society is to vaccinate the remaining portion in order to limit the impact, resulting in an overall loss of -11 (left bottom). However, this is a worse outcome than the one in the left top corner of -2. 

Using incentives to achieve optimal equilibrium

In a free society, there is little option for compulsory vaccination and it is up to the individual to make the decision; incentives should therefore be provided to make vaccination more attractive. Assume this creates an additional benefit of +2, as shown in Table 4.

 

web_p39_The-vaccine-dilemma_Table-4.                         

As a result, the optimising strategy for the individual has changed from Refuse to Vaccination. This leads to a better overall outcome in Table 3, as the top left is now the new equilibrium.

This shows that current policies for providing positive incentives (such as easier overseas travel and access to certain events) for vaccinated individuals will result in a better outcome for society as a whole. The incentives should be strong enough to limit the size of the group refusing the vaccine to the extent that this group’s choice does not impact the outcome of society as a whole.

Servaas Houben is an actuarial manager at ERGO Belgium

Image credit | Ikon
ACT Sep21_Full LR.jpg
This article appeared in our September 2021 issue of The Actuary .
Click here to view this issue

You may also be interested in...

web_p32_New-tricks_People-selling-tobacco-leaves-in-Zimbabwe_CREDIT_Getty-1210188895.jpg

New tricks: pricing microinsurance products in Zimbabwe

Tawanda Chituku discusses his experience pricing microinsurance products in Zimbabwe
Wednesday 1st September 2021
Open-access content
web_p34-35_The-lake-of-fire_Pit-crater-Nyiragongo-Volcano-DRC_CREDIT_Getty-140189982.jpg

Lake of fire: insurance penetration in risk zones

Brian McGregor explores how insurers can increase insurance penetration in risk zones, such as the area around the Mount Nyiragongo volcano
Wednesday 1st September 2021
Open-access content
web_p40_HACK-to-the-Future_Text-Effect.jpg

Hack to the future

Louise Pryor, Colin Dutkiewicz and Krishna Kumar Shrestha reflect on the ICAT’s recent R number hackathon, and what it means for the profession’s future skillset and role in society.
Wednesday 1st September 2021
Open-access content
web_p30-31_The-

The new 'R' word

What has the COVID-19 pandemic taught us about business resilience during a crisis? Dermot Grenham and Isaac Alfon explain
Wednesday 1st September 2021
Open-access content
web_p27_Moral-fibre_CREDIT_iStock-671039110.jpg

Moral fibre

Anthony Asher provides a critique of the dominant thinking within risk culture, and explains why courage will play an important role in forming a more virtuous approach
Wednesday 1st September 2021
Open-access content
web_p22-23_All-together-now_Network-conceptual_CREDIT_Istock_876848746.jpg

All together now: modelling claims using federated learning

Małgorzata Śmietanka, Dylan Liew and Claudio Giorgio Giancaterino demonstrate how to model claims anonymously using federated learning
Wednesday 1st September 2021
Open-access content

Latest from Health care

yf

Animal crossing: the threat of zoonotic diseases

Prachi Patkee and Adam Strange discuss what the rising threat of climate-driven communicable disease means for insurers
Wednesday 30th November 2022
Open-access content
hb

Boiling point: the effect of rising temperatures on future mortality

As quantifying climate risk exposure becomes increasingly important, Dan Gill, Rajinder Poonian and Alex Harding investigate the effect of rising temperatures on future mortality
Wednesday 2nd November 2022
Open-access content
vb

Interview: Professor Paul Dalziel on changing the focus of economies from growth to wellbeing

Paul Dalziel talks to Alex Martin about the true purpose of economics and the lessons we can draw from the 2019 New Zealand wellbeing budget
Wednesday 2nd November 2022
Open-access content

Latest from General Features

yguk

Is anybody out there?

There’s no point speaking if no one hears you. Effective communication starts with silence – this is the understated art of listening, says Tan Suee Chieh
Thursday 2nd March 2023
Open-access content
ers

By halves

Reducing the pensions gap between men and women is a work in progress – and there’s still a long way to go, with women retiring on 50% less than men, says Alexandra Miles
Thursday 2nd March 2023
Open-access content
web_Question-mark-lightbulbs_credit_iStock-1348235111.png

Figuring it out

Psychologist Wendy Johnson recalls how qualifying as an actuary and running her own consultancy in the US allowed her to overcome shyness and gave her essential skills for life
Wednesday 1st March 2023
Open-access content

Latest from Servaas Houben

hgv

Exchange of ideas: IFRS 17 implementation in the Caribbean

Servaas Houben considers how IFRS 17 principles could benefit insurers in the Caribbean – and what European insurers could learn from the region when it comes to implementing the standard
Wednesday 31st August 2022
Open-access content

Latest from September 2021

web_boardgame-Go_credit_iStock-182187699.png

Environment agents: Introduction to reinforcement learning

Jonathan Khanlian outlines how the machine learning technique of reinforcement learning can be viewed from an actuarial perspective
Thursday 2nd September 2021
Open-access content
web_p18_Coughing-up_Carbon-Taxing--Currency-with-chimney-bellowing_CREDIT_Mark-Airs_Ikon_00024955.jpg

Coughing up on carbon taxation

Trevor Williams gives an economist’s view of carbon taxation
Thursday 2nd September 2021
Open-access content
Obituary

Obituary: Jim Galbraith

It was with much sadness that we learned of the premature passing of our friend, university classmate and fellow actuary Jim Galbraith. He died suddenly in April 2021 at the age of just 58, leaving family, friends and colleagues devastated.
Thursday 2nd September 2021
Open-access content
Share
  • Twitter
  • Facebook
  • Linked in
  • Mail
  • Print

Latest Jobs

Actuarial Contract Opportunities - Life Insurance

United Kingdom, Ireland and Remote
Competitive
Reference
148599

Pricing Manager (Mid-Corp)

London (Central)
£75000.00 - £90000.00 per annum
Reference
148749

Head of Insurance Pricing Risk

London (Central)
£100000.00 - £130000.00 per annum
Reference
148748
See all jobs »
 
 
 
 

Sign up to our newsletter

News, jobs and updates

Sign up

Subscribe to The Actuary

Receive the print edition straight to your door

Subscribe
Spread-iPad-slantB-june.png

Topics

  • Data Science
  • Investment
  • Risk & ERM
  • Pensions
  • Environment
  • Soft skills
  • General Insurance
  • Regulation Standards
  • Health care
  • Technology
  • Reinsurance
  • Global
  • Life insurance
​
FOLLOW US
The Actuary on LinkedIn
@TheActuaryMag on Twitter
Facebook: The Actuary Magazine
CONTACT US
The Actuary
Tel: (+44) 020 7880 6200
​

IFoA

About IFoA
Become an actuary
IFoA Events
About membership

Information

Privacy Policy
Terms & Conditions
Cookie Policy
Think Green

Get in touch

Contact us
Advertise with us
Subscribe to The Actuary Magazine
Contribute

The Actuary Jobs

Actuarial job search
Pensions jobs
General insurance jobs
Solvency II jobs

© 2023 The Actuary. The Actuary is published on behalf of the Institute and Faculty of Actuaries by Redactive Publishing Limited. All rights reserved. Reproduction of any part is not allowed without written permission.

Redactive Media Group Ltd, 71-75 Shelton Street, London WC2H 9JQ