The Prisoner’s Dilemma in the Age of Lockdown

Illustration by Allen B Thangkhiew

The Prisoner’s Dilemma, is a quintessential thought experiment, taught to any Social Science student as a classic example in an introductory Game Theory class. It was originally hypothesized by Merrill Flood and Melvin Dresher in 1950, and was formalized mathematically, by Albert Tucker in the same year.

The game proceeds as follows: Two partners in crime are caught and are imprisoned in separate cells, with no means of communicating with the other. The police do not have enough evidence to convict them of a recent larger crime, but have enough to convict them of an older and smaller crime. The police then make them an offer. Each is given one of two choices – To confess that the other committed the crime, or to remain silent.

If both confess, they each serve 2 years in prison for the larger crime. If one confesses, but the other remains silent, the former will be set free, while the latter will be sentenced to 3 years, and vice versa. If both remain silent, they both serve only 1 year, for the smaller crime.

Game Theory predicts that if the partners were rational and self-interested, both would choose to confess, rather than to remain silent. This is because, remaining silent comes with the risk of being betrayed by a confessing partner.

With the recent coronavirus outbreak, and the onslaught of lockdowns and curfews imposed by the Indian government, citizens are now faced with the challenge of living in a new post-virus world. Social Distancing, Quarantine, and Isolation are becoming the norm, rather than the exception, in the fight to contain the spread of the virus. By tolerating temporary setbacks, that is, briefly surrendering the enjoyment of public goods and services, outdoor recreation, and physical contact – things that we normally take for granted – the virus spread can soon be curbed. In particular, the rate of growth of the virus in India, has declined by about 40% (or about 6 percentage points), from a growth rate of approximately 16% pre-lockdown, to 10% post-lockdown.

Yet, we observe widespread dissonance among the people and the state. We hear of massive crowds at the Sabzi Mandi in Delhi; of large religious gatherings in Murshidabad in West Bengal; and of hundreds, if not thousands, of migrant workers from the cities, defying lockdown orders, to return to their homes. We see educated and woke individuals often failing to take precautionary measures directed towards their own and others’ safety. We speak of Hedonism prevailing over Collectivism – collective action, taking a backseat in the pursuit of instant gratification.

The problem at a glance, appears to be the lack of faith of the people, in institutions. On closer examination however, the problem is a lack of trust in one another – the fear of betrayal, and of lagging behind in the ‘competition’, whatever it may be – akin to the Prisoner’s Dilemma problem, where one partner walks free, while the other suffers.

Let us consider the following Lockdown Game, modelled along the lines of the Prisoner’s Dilemma: We have two players – Me and You, with payoffs m and y, respectively; each having two strategies – Stay Home, and Go Out. The payoff matrix is illustrated below, where the payoffs are listed in terms of utils as (m,y) for each outcome (Utils are a measure of satisfaction). For example, if Me chooses to Stay Home and You chooses to Go Out, we are looking at payoffs in the second cell, that is, (-1,2). This implies that Me gets a negative payoff of -1 util from staying home, and You gets a positive payoff of 2 utils from going out.

To solve the game, we begin by looking at Me’s perspective. If Me chooses to Stay Home, You’s best response is to Go Out, as going out gives You a higher payoff of 2, as compared to staying home and getting a payoff of 1. Similarly, if Me chooses to Go Out, You’s best response is again, to Go Out, as going out gives You a higher payoff of 0, as compared to staying home and getting a negative payoff of -1 (Best response payoffs have been underlined in the payoff matrix). Therefore, You, has a dominant strategy to Go Out. Given that Me and You are symmetric in strategies and payoffs, we similarly deduce that Me’s dominant strategy is to Go Out.

Thus, in the game of Lockdown, we see that both Me and You, playing rationally, choose to Go Out, both getting a payoff of 0 each, rather than choosing to cooperate and Stay Home, both getting a payoff of 1 each, even if it is in their best interests to do so. It is the demonstration effect of breaking lockdown protocol, and the fear of missing out, that push both Me and You to go out, thus resulting in an inferior equilibrium.

Envy is the cause of the trust deficit that human beings experience, when choosing to follow lockdown protocol. As we move forward in these testing times, we, as members of a collective consciousness, must realize that the exponential growth of the virus, is not to be looked upon as a non-cooperative game, but a cooperative or collaborative one. It would be constructive for everyone to behave as if they signed an implicit social contract, rather than act out of selfish self-interest. Foresight can go a long way in enabling us to look beyond static games, and into dynamic games – One must now view the world, as one with an infinite horizon, and accept the fact that social distancing is the new normal. The road ahead, for policymakers too, will not be an easy one, as they are now tasked with designing new institutions for a new world, as future outbreaks may have the potential to obliterate, if not cripple the entire politico-socio-economic structure. As individuals, we must take into account lessons such as these, because this is not a game that we can afford to lose.

A Note on the Payoff Matrix:

When Me and You play (Stay Home, Stay Home), both Me and You benefit from social distancing, and obtain a payoff of +1 each.

When Me and You play (Stay Home, Go Out), Me envies You, and obtains a payoff of -1, while You gets to enjoy, let’s say fresh air, and obtains a payoff of +2; and vice versa for when Me and You play (Go Out, Stay Home).

When Me and You play (Go Out, Go Out), both Me and You enjoy fresh air, but with the fear that by violating social distancing norms, the other may have contaminated the air with the virus. There is no envy of the other here, only fear balancing out the benefit of fresh air, and thus, Me and You obtain a payoff of 0 each.

 

Author: Daniel Challam

Daniel Challam is a freelance writer and researcher, currently based in Delhi. He is a Postgrad from the Delhi School of Economics, and an Undergrad from Ramjas College, Delhi. A New Institutionalist by training, he loves taking models to the real world (and secretly enjoys proving them wrong, as long as they’re not his). His current interests lie in Political and Institutional Economics, Public Economics, and the Economics of Discrimination.

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