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Vaccination Case Analysis Using Game Theory Case Study

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Updated: Jul 8th, 2021

Game theory has been applied to a wide variety of phenomena that are observable in the modern world. As Goolsbee, Levitt, and Syverson (2016) point out, game theory is valid for many human and non-human interactions. One of the examples of such interactions is the vaccination dilemma, which has been studied extensively, especially with respect to epidemics (Iwamura & Tanimoto, 2018). Given the increase in the rates of measles that is observed globally (UNICEF, 2019), this topic is very relevant nowadays. The present study will focus on a particular case of vaccination that is covered by UNICEF (2019) and analyze the specifics of strategic decision-making in it with the help of the game theory.

The theoretical framework for the case study can be summarized as follows. According to Goolsbee et al. (2016), game theory is an economic theory that is used to investigate strategic decisions made by humans in a situation when multiple actors are involved. Vaccination, from this perspective, is a game that has many players; typically, their number can be limited to the community in which the decision-maker lives (Iwamura & Tanimoto, 2018). The strategies include either vaccinating or not vaccinating; arguably, the third strategy of alternative safety measures can be listed, but it is not relevant for the studied case (Ida & Tanimoto, 2018). The payoff is either catching or not catching the disease; commonly, the number of people who do not vaccinate increases an individual’s risk of contracting the disease (CDC, 2018a). Furthermore, as shown by the analysis performed by Iwamura and Tanimoto (2018), vaccination is an example of repeated games: participants make decisions simultaneously, but they get to repeat the process, which is why they can observe the outcomes of different decisions for themselves and others.

The following information is relevant for the analysis. When reporting some information about the recent immunization effort in Ukraine, UNICEF (2019) mentions the case of Uliana Dziuba. Uliana Dziuba is a mother who used to be resistant to vaccination but changed her mind when one of her children got measles. Dziuba points out the impact of anti-vaccination efforts on her prior decisions and explains why she changed her mind. This case is interesting in that it can be used to illustrate the dilemmas that an individual parent can face when scheduling vaccination for their child during a crisis and non-crisis situation.

Table 1. Vaccination Game in the Absence of Epidemics.

Other players
An individual player Vaccinate Not vaccinate
  • Likely outcomes for the individual: no risk of disease for a cost (depending on the health insurance/governmental approach to vaccination)
  • Possible risks for the individual: negative outcomes of vaccination (very unlikely)
  • Outcomes for all players: possibility of eradicating epidemics and diseases
  • Likely outcomes for the individual: no risk of disease
  • Possible risks for the individual: negative outcomes of vaccination (very unlikely)
  • Outcomes for the rest: high risks of disease, epidemics
Not vaccinate
  • Likely outcomes for the individual: low or no risk of disease at no cost
  • Possible risks for the individual: none
  • Outcomes for all players: possibility of eradicating epidemics and diseases
  • Outcomes for all players: high risks of disease, epidemics, illnesses will not be eradicated

Initially, Dziuba made decisions about vaccination during a non-crisis situation. A simple representation of her dilemma with players, strategies, and payoffs can be found in Table 1. As can be seen from it, an individual player is faced with the decision of either vaccinating a child or not. In the first case, the likely outcome is the child not being harmed; the unlikely outcome consists of the child suffering from the side effects of vaccination. For example, the MRR vaccine, which is the one that is used against measles, has an extremely rare possibility of causing a serious allergic reaction, febrile seizure (4 out of 10000 chance for children younger than two years), and immune thrombocytopenic purpura (1 in 40000) (CDC, 2018b). CDC (2018b) emphasizes the fact that no connection between MRR and autism has been found by multiple studies. As children grow older, the possibility of particular side effects may slightly increase.

In summary, the likelihood of negative outcomes of vaccination is not non-existent, but it is very low. The costs of vaccines vary, especially for different countries, and governments usually try to support vaccination by relieving the financial burden, which is the case for Ukraine (Ethgen, Cornier, Chriv, & Baron-Papillon, 2016; United Nations Ukraine, 2017). Therefore, Dziuba probably did not have to pay, which is why the price was not a major concern for her (aside from the traveling costs to get to the clinic).

If an individual player chooses not to vaccinate a child, they avoid the negative consequences of vaccination completely and do not have to pay anything. However, the future safety of their child depends on the actions of the rest of the players, and the more of them refuse to risk vaccination, the more likely a vaccine-resistant family is to experience the diseases that vaccines are supposed to prevent (CDC, 2018a). CDC (2018a) also points out that vaccinated individuals can travel abroad to countries where particular diseases are not uncommon, bringing them to a country that has eradicated them and endangering unvaccinated people.

Thus, in case he or she chooses not to vaccinate, the outcomes of the actions of an individual player depend heavily on the actions of other players. On the other hand, vaccination guarantees the reduced risk of contracting a disease for the vaccinated person regardless of the strategies of the rest of the players, but the individual risks of vaccination are also present every time an individual player chooses to vaccinate. If a person recognizes the fact that the risks are minimal, vaccinating should be viewed as the dominant strategy. However, not all players are going to view the risks as justified (UNICEF, 2019), which is why they may not agree with this idea. Moreover, the loss aversion bias is important: the risks of vaccines may be perceived as more significant because humans subconsciously choose to reduce losses (Goolsbee et al., 2016). Dziuba is a prime example of a person who used to consider vaccinating too dangerous.

However, as the situation in Ukraine was moving toward an epidemic, the context of the game changed. The likelihood of a person contracting a disease had increased (partially as a result of the prior decisions of multiple players not to vaccinate) (UNICEF, 2019). From this perspective, the case may exemplify a situation in which the individual player has observed the game for several cycles and was made aware of the consequences of the lack of vaccination (for Dziuba’s, those consequences were experienced by one of her children). Based on this new information about the potential payoff of her choice, Dziuba made the decision during a new cycle, choosing to vaccinate her children.

It should also be pointed out that many of the players in the vaccination game are not exactly reasonable. First, vaccination typically occurs with children’s health at stake. The decision of the studied player is going to impact her children, which means that it has a very strong emotional component. Aside from the fear, responsibility, and potential guilt connected to the possibility of harming one’s child, it is not unlikely that for many people, the short-term safety of their own children may appear more important than that of other people. Naturally, this idea is self-defeating since once many people make this choice, infections like measles become sufficiently dangerous to harm unvaccinated people again (CDC, 2018a; UNICEF, 2019). However, some people may not fully understand this potential outcome.

Indeed, many of the players may be exposed to misinformation, which is especially true for the illnesses that are now uncommon: people who have not witnessed them may find it difficult to understand their consequences. In the case of Dziuba, this issue was relevant: she highlights the impact of an anti-vaccination campaign on her decision not to vaccinate. However, she also references the impact of her child falling ill on her choice to vaccinate. Thus, while applying game theory to vaccination, it is important to remember the emotional and educational factors that can make the maximin strategy relevant (Goolsbee et al., 2016). In the case of Dziuba, in order to minimize the possibility of losses, she needed to vaccinate her children, which she did.

As pointed out by Iwamura and Tanimoto (2018), when describing the “vaccination game,” it is possible to oversimplify it by failing to take into account the context and specifics of vaccination, especially the emotional response of humans to epidemics. By investigating the story of Dziuba, it is possible to consider vaccination-related behavior both prior to a crisis and during it. As a result, the case highlights the impact of this emotional response, as well as the fact that humans are not always rational, which is especially important for economic theorists to consider. Apart from that, the analysis demonstrates the applicability of game theory to strategic thinking during vaccination decision-making, showing its usefulness for the task.


CDC. (2018a). Web.

CDC. (2018b). Measles vaccination. Web.

Ethgen, O., Cornier, M., Chriv, E., & Baron-Papillon, F. (2016). The cost of vaccination throughout life: A western European overview. Human Vaccines & Immunotherapeutics, 12(8), 2029-2037. Web.

Goolsbee, A., Levitt, S., & Syverson, C. (2016). Microeconomics (2nd ed.). New York, NY: Worth Publishers.

Ida, Y., & Tanimoto, J. (2018). Effect of noise-perturbing intermediate defense measures in voluntary vaccination games. Chaos, Solitons & Fractals, 106, 337-341. Web.

Iwamura, Y., & Tanimoto, J. (2018). Realistic decision-making processes in a vaccination game. Physica A: Statistical Mechanics and Its Applications, 494, 236-241. Web.

UNICEF. (2019). Web.

United Nations Ukraine. (2017). Ukraine’s efforts to stop measles outbreak continue as case total increases. Web.

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