Game Theory and Pandemics


By Sakshi Dhawan and Kritika Chakrabarti

Game Theory

Microeconomics is the study of the behaviour of individuals and firms, as well as their interactions with one another. In some ways, it is concerned with a maximisation of individual and firms’ payoffs. Certain foundations of microeconomics depend on a fundamental assumption when determining the payoffs between any two economic actors: that there is no consumption externality i.e., the consumption of one actor does not increase or decrease the payoffs of the other actor. As you can probably already tell, this assumption does not hold up well in a host of different circumstances. An example of a positive externality would be vaccination – when an individual is vaccinated against an infectious disease, it helps to prevent the spread of this disease, benefiting others. Such instances require strategic thinking, and therefore draw on the use of Game Theory.  

Game Theory is the study of a collection of models of strategic interaction between players, premised on rational choice or maximising behaviour by the agents. It is, in many ways, the science of strategy that is concerned with the outcomes that are produced by this interaction, based on the preferences of the players. Games can come in two primary forms: strategic games or extensive form games. A strategic game is one in which players simultaneously choose actions and an extensive form game is one in which actions are chosen sequentially. The applications of game theory are not limited to economics. While initially developed for use in the domain of economics to understand certain economic behaviours that result from the behaviours of firms, consumers and markets, game theory is now used across a wide array of domains such as biology, philosophy and politics.

Game Theory and Public Policy

Game Theory plays an important role in public policy as well, through social dilemmas. A social dilemma refers to a situation within which the Nash Equilibrium leads to outcomes that are below the Pareto optimal. A point is said to be Pareto Optimal if there is no way to reallocate resources to make one individual better off without making at least another individual worse off. Social dilemmas tend to result in such outcomes because they are characterised by situations in which “there is a conflict between individual and collective interest”. A more detailed definition of a social dilemma is as follows:

A social dilemma is defined by two properties:

  1. Each individual receives a higher payoff for a socially defecting choice than for a socially cooperative choice, no matter what  the other individuals do, but
  2. All individuals are better off if all cooperate than if all defect (Kollock, 1998)

Due to the manner in which Social Dilemmas are structured, they often promote competition over cooperation—even if human beings instinctually prefer cooperation over competition—by providing a higher payoff for an individually socially defecting choice, social dilemmas create incentive for competition. These preferences can further be exemplified by priming the dilemmas in certain ways. For instance, participants tend to play more competitively when the game was called “Wall Street broker game” than when the same game was called “community game” (Ross and Ward, 1995).

With this view in mind, public policy can be used to change the “competitive” outcomes of social dilemmas into “cooperative” ones: from a Nash Optimal outcome to a socially optimal one. Game theoretic models have been used extensively for public policies regarding voting, fiscal competition in decentralised political systems, an international response to pollution, taxation and vaccination programs. Game theory is also used in conjunction with behavioral economics to tailor a game theoretic approach that is based on how individuals actually make decisions as opposed to the traditional utility maximising choice.

Modelling Pandemics Using Game Theoretic Models

The use of Game Theory to model a pandemic is not novel in nature. There is, however, a significant departure from the traditional games that most of us are familiar with: as opposed to players having complete information while forming their strategy, in the case of a pandemic, players have incomplete information. As a result of this incomplete information, the payoffs that individuals perceive to have for themselves and others change, and are inconsistent in nature. 

In a paper that was the 2015 winner of The Bellman Prize, researchers attempted to model the impact that individuals’ behaviour can have on the spread of an epidemic. The authors’ arguments are based on two fundamental premises: first, that individuals’ responses to an epidemic are contingent on their perception of how likely they are to get affected, and secondly, this perception is not constant in nature and changes based on the information that they receive. For this, they contrast the responses to the H1N1 influenza (swine flu) and the Ebola epidemic. At the time of the swine flu, the information being circulated by mainstream media contained projections for high rates of infection, as a result of this, the public responded by “taking precautions and behaving sensibly.” During the Ebola epidemic, however, there was a lack of media attention on the disease and its spread, initially resulting in a lower perception of risk by the public. As the epidemic progressed, coverage of the epidemic changed to show Ebola as a serious disease, and so did the public’s risk perception. There was a difference in public compliance to policy as a result of incomplete information.

In the game theoretic model proposed by the authors of this paper, they suggest that individuals’ behaviour during an epidemic depends not only on their risk perception but also on the behaviour of other individuals. Changes in behaviour are undertaken based on other individuals, which is why a situation with an equal split of responsive and unresponsive individuals gives policymakers a positive chance to change behaviour. Therefore, for such a model of strategic interaction, it is imperative for policymakers to ensure that “accurate information is disseminated quickly”, so that there can be greater clarity on the dominant strategy, and individuals’ behaviour is more in line with that of the “rational decision maker” (RDM).   

Covid-19

According to Richard Holden, Professor of Economics at the University of New South Wales, we can be thought of in a game with the virus. The virus, the community and the policymakers (their participation is contingent on the degree of compliance with their policies) are all players within this game with fairly straightforward payoffs. For the virus, the pay off involves infecting people. For policymakers and the community, the payoff is relatively complex, involving different outcomes for public health and the economy. On an individual level, payoffs can change based not only on the outcome for the aforementioned variables, but also on the individual risk of infection, the cost of social distancing and other preventative measures and so on.   

The action profile that the community holds depends to some degree on the policymakers, and can involve cooperation. In this case, social isolation is a kind of cooperation and can have real costs for your own happiness, but it protects those around you from an exponentially growing virus. While defecting is tempting and there’s an immediate payoff to the individual, cooperation makes everyone better off. In areas where a strategy of lockdowns against the Covid-19 virus has been adopted, the curve of confirmed cases is flatter than that in areas where such measures have either not been adopted or were adopted too late. 

Prisoner’s Dilemma : A Covid-19 model

Many of us are well aware of the basic game theory model called the prisoner’s dilemma and if we look closely, the novel coronavirus pandemic seems like a real time situation that can be fitted well into this model. The prisoner’s dilemma is basically a situation in which there is an incentive to make a choice that does not produce the optimal result for the group. Some aspects of this pandemic reflect the same, such as the decision to self-quarantine during a pandemic looks a lot like a move in a multiplayer version of this game. One can either cooperate, and do something that costs a little while helping those around, or defect, and bring himself/herself a small benefit at a greater cost to those around him/her. 

A common practice of hoarding of essential goods or in other words, stockpiling is being widely observed among the panic stricken citizens of almost every affected country. For example, data reflects that in the UK, household and pet care items have shown the biggest year-on-year increase of 65% in sales while ambient groceries experienced a 62% hike.

This is nothing but basic risk assessment that is being done by individuals in the times of a crisis such as this. Even though everyone may not be voluntarily choosing to stockpile, it is very natural for each of us to be uncertain and take all possible precautions. 

If we consider a two-player model, three situations may arise –

  1. Both of them hoard
  2. One of them hoard
  3. None of them hoard

Clearly, situation 1 leads to rise in price levels due to increase in demand and situation 2 leads to shortage of goods for one of them. Thus, the optimum decision is for both to not hoard such that the price level remains the same (from the demand side) and there is no shortage making both of them better off. However, a rational individual will choose to hoard as a precaution, for he is unsure of the other player’s decision and if he chooses to not hoard and the other player chooses otherwise, then he might not be left with any items to buy.

So now the question before us is: are people acting irrationally? At a collective level, stockpiling is gradually leading to shortages of goods in the market. But in a direct sense, people are acting rationally and it becomes optimal rather than suboptimal to start stockpiling if everyone else does so, because their stockpiling creates the very supply problem they are trying to avoid in the first place. Thus, this situation clearly conforms to the idea of prisoner’s dilemma.

While trying to solve situation-based problems using game theory, we must first analyse the problem itself by asking relevant questions like who are the relevant players in the game? What incentives do they respond to? How are each of their choices inter-linked? And whether or not they can be trusted to make all cost-benefit decisions. 

In the current scenario, the main players are the citizens and the government whose choices make the difference and to a large extent play a crucial role in curbing the pandemic which constructs the model in question. 

Again, focusing on the problem of hoarding, the UK government had suggested that supermarkets would be advised to allow only 10 people in at a time, alongside the already implemented two or three items per person rules to tackle induced shortages. These policies are based on a cynical intuition that the majority of shoppers are irrational hoarders and that they would purchase these items whatever the price, and consequently lead to inflation. On the other hand, by increasing prices on certain goods like toilet paper, individuals would opt to buy in smaller volumes, leaving more stock on the shelf and increasing buyer confidence that there is no shortage. This is nothing but the government, a player trying to play the game of incentivisation in the game theory model. 

There are several other game theory models that can be used to analyse the current crisis and its application in policy-making is being widely explored in order to make correct and well-informed decisions which will maximize welfare, both social and economic.

References

http://blogs.oregonstate.edu/econ439/2014/02/10/game-theory-policy/

https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/applications.html

http://faculty.washington.edu/jtenenbg/courses/tgh303/f12/socialDilemmaFormal.html

https://opentextbc.ca/socialpsychology/chapter/how-the-social-situation-creates-conflict-the-role-of-social-dilemmas/

https://www.exploring-economics.org/fr/decouvrir/an-introduction-to-game-theory-in-public-policy/

https://www.sciencedirect.com/science/article/pii/S0025556412000892

https://blogs.cornell.edu/info2040/2016/09/16/game-theory-in-the-context-of-epidemics/

https://theconversation.com/vital-signs-a-lesson-from-game-theory-the-coronavirus-contrarians-ignore-135821

https://www.philosophytalk.org/blog/game-theory-and-covidiocy

https://www.adamsmith.org/blog/covid-19-and-game-theory

https://www.essentialretail.com/news/covid19-grocer-sales-stockpiling/

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