What Game Theory would say about those tourists thronging Mall Road – and about the possibilities of a third wave?
Abhishek Ananth and Payal Seth | September 23, 2021
The brutal second wave of the COVID-19 pandemic in India has left a significant death toll in its wake. Health experts advise that the imminent third wave can be delayed by following simple measures like wearing a mask and engaging in social distancing. However, near the end of the second wave, we witnessed a surge of tourists thronging the Mall Roads of Manali and Shimla, blatantly refusing to adhere to these safety protocols. Why are people abandoning caution despite knowing that it will only expedite the arrival of the third wave? In this article, we use a game-theoretic approach to rationalise the seemingly irrational decision-making to explain why the Manali holidayers are ignoring scientifically-backed safety measures.
We start by defining the economic concept of externality, i.e., cost imposed on or benefit received by a third party, who did not agree to partake in it. The former is referred to as the negative externality, while the latter is a positive externality. In the context of COVID-19, the act of wearing masks, practising social distance or getting vaccinated levies a positive externality on society as it decreases the probability of transmitting the infection. Likewise, negative externality occurs when individuals fail to follow these protocols.
Now, assume that people are cognizant of a specific probability (say x, x>0) with which they might get infected with the coronavirus when everyone is following covid safety protocols. However, with every person that flouts these covid safety measures, everyone’s infection probability increases by a very small amount (say y, y>0). As an example, when two people violate covid safety measures, everyone’s probability of getting infected becomes x + 2y. We also assume that the preferred outcome for the person deciding to holiday in Manali (now addressed as player 1 of the game) is to explore the vistas of Manali while avoiding catching COVID-19. To ensure this outcome, player 1 can play one of two strategies: either stay at home or go to Manali. The rest of the society (say, 1,000 people), who we collectively refer to as player 2, are also facing the same two strategies. The probability of the impending COVID-19 third wave will rest on the decisions of everyone within society.
If player 2 (the rest of the society) decides to stay in, then player 1 has to choose between the strategy of staying in or going to Manali. If player 1 also decides to stay in, the probability of infection remains small but positive x for everyone. However, he/she will be unable to experience the perceived benefit of vacationing in Manali. Next, if player 1 decides to go to Manali, while everyone else stays tucked in their houses, then everyone’s infection probability increases to x+y. Player 1 might decide that the joy of going to Manali outweighs the small increase in infection probability (from x to x+y) that (s)he faces. So, if player 2 stays in the house, then player 1 will go to Manali.
Now, what if player 2 also decides to venture out, then should player 1 stay in or go out? If player 1 decides to stay in, s(he) knows that the infection probability is now x + 1000y which can be quite high even when y is small. If player 1 decides to step out, then the risk of getting infected is x + 1001y. Since Player 1’s risk of infection only increased by a small magnitude (y), player 1 is tempted to head out too. Therefore, if player 2 decides to go out, then player 1 will decide to do so as well.
Remember that player 2 subsumes the 1,000 individuals who are solving this game: if no one is heading to Manali, then my going out will not affect the probability of the impending third wave, and if all of them are going out, then the third wave will inevitably come, leading to more lockdowns. Since I would be unable to travel then, the best course of action, even when others are out, is still to travel. This is the issue with negative externalities: it leads to the ‘tragedy of the commons’, a situation in which individuals are unable to internalise the externality they impose on the others (i.e., abandoning caution while travelling to Manali) and hence overindulge in the activity that is going to cost the society, and in turn, their future self (i.e., accelerating the onset of third-wave).
Just as economics is helpful in explaining the rationale behind the seemingly irrational behaviour, it is also useful to provide useful public health policy solutions. Games that exhibit coordination problems like this (the inability of individuals to come together for the benefit of society), can be resolved by preferring sticks, rather than carrots. The state governments have already initiated imposing penalties for flouting the safety measures like regulating the entry of tourists or imposing fines of Rs 5,000 for not wearing masks. This article also serves to demonstrate the complex challenges that epidemiologists face in predicting the timing of upcoming waves, as each individual is simultaneously making decisions in response to others’ decisions. When we further add other variables like the rates of vaccination, demography, social structures and political climate to our current game, the analysis becomes more complicated but much more realistic. Indeed, the plethora of forecasts we see regarding the third wave are a direct consequence of the ever-changing variables used in these models. This is why, dear readers, we recommend keeping a constant lookout for new predictions to continue staying safe, as each offers something new!
Abhishek Ananth is a post-doctoral fellow at the University of Geneva, Switzerland.Payal Seth is a consultant at the Tata-Cornell Institute, Cornell University, USA.
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