Dr Srinivas Chilukuri
Sr. Consultant Radiation Oncologist
Apollo, Chennai

Dynamics of cooperation during the pandemic, based on game theory

It is now clear that the COVID-19 pandemic has affected physical, social, and economic health of the humankind in an irreversible and unprecedented way. Within a short span of time, it has managed to surpass all geo-political boundaries with an unmatched pace. It has also slowed down the ever-increasing pace of humans, at least temporarily, with most countries in complete lockdown, some more intense than others. This approach of suppression by virtue of major lockdowns was the most sensible in the current scenario, but its success would heavily depend on our (social animal) behavior, both at the individual and at the community or country level.

At the individual level, the more animalistic we are, that is more we satisfy the urge for instant gratification and think of our primal needs, more is the irreversible damage to our society.

More social we are, that is more we think about our society with respect to long-term outcomes, more is the chance of coming out with limited damage. Even in free societies or modern democracies, lockdowns or curfews can be planned and implemented, but can they be robustly enforced? Can it be achieved through persuasion rather than threats? Although most individuals display a systematic bias to adhere to the recommendations and cooperate, the personal ambitions and insecurities dictate the deviant behavior.

This is also predicted by the mathematical game Prisoner’s Dilemma, which based on game theory is a paradox in strategic decision making, in which two players acting in their own respective self-interest do not produce the optimal outcome. For example, in this mathematical game, two partners of a criminal gang are imprisoned for performing two separate acts of a minor crime and are locked up in solitary confinement with no means of communication.

Although authorities suspect that they have committed a bigger crime together, they have no evidence to prosecute them. The authorities offer a deal to each one of them. If one of them betrays the other by confessing, the other would be imprisoned for 10 years and the one who confesses, would be let free. If both of them, do not confess or betray each other they get out in 2 years, and if both confess and betray each other, both would be imprisoned for 5 years. If you draw a matrix, the best-case scenario would be to cooperate with each other and get out in 2 years, but individually for each, regardless of what other does, the optimal choice is to confess and betray the other. This scenario of both confessing is called Nash equilibrium (after John Forbes Nash), which is a stable state of a system, in which no player can gain from a change of strategy assuming other is not changing his strategy.

In the context of this pandemic, individually there is little motivation for majority to adhere to cooperation or to lock down norms, despite the fact that adherence is in their, and their community’s, best interest just like the players in the Prisoner’s Dilemma. This is applicable in democratic communities, where there is abundance of individual rights and freedom, and not valid for authoritarian regimes where penalties or punishment play a dominant role in people’s behavior. Even in democratic communities, the necessary behavioral changes can be brought through self-imposition, either by inspiration or by fear.

In this case, fear is a potent weapon but the challenge is not to trigger panic as it brings out animal instincts. Irrespective of who we are, our behavior is driven by our biggest insecurities or fear at any point of time. Again, applying the principles of game theory in the context of the prisoner’s dilemma, fear of a consequence can become a bigger motivation to choose a particular strategy.

Fear can be productively instilled through dissemination of right information. Thanks to the social media, dissemination has never been easier, and the only challenge is to separate the valuable information from the milieu of propaganda and individual opinions.

At the community level, this pandemic appears to be a crisis of anticipation capacity by various governments internationally. There was a clear lack of internationally concerted efforts at the beginning of the epidemic due to lack of information on one hand and callous attitude on the other.

In the midst of crisis, already a blame game has started with each side dedicating precious time and resource. This adds to the friction that has already existed due to the ongoing trade wars. Again, principles of game theory can be applied to understand the stance taken by the governments and predict their strategies.

In the war of attrition (proposed by John Maynard Smith), consider an all-pay auction where each player compulsorily pays his bid, and the player with the highest bid wins a resource. Assuming the value of the resource being X and the value of bid being b, the payoff is b if he loses and Xb if he wins.

Since each of them has to pay the bid, irrespective of their success, it is in each player’s best interest to bid the highest amount and win. Hence, it is possible that value of b is more than X that means paying more than the value of the resource, which actually seems foolish.

This is what happens in the real world. Sometimes to gain in geo-political game of one-upmanship, countries tend to pay a heavy price eventually to lose. Also, each leader in his own community has a huge incentive to cheat his community or cartel to go one up against the local competition.

However, there is a case for collaboration based on the mathematical non-zero-sum game or win-win strategy, where a collaborative strategy accommodates the interest of each player to derive maximal benefit to each other. Going back to the prisoner’s dilemma, just imagine both the prisoners adhering to a pre-decided binding pact that they would cooperate with each other in times of crisis for mutual benefit. They would both get away with minimal punishment.

Although, it is easy to be pessimistic in the season of gloom and believe in Hobbesian state of nature theory, which states that each human seeks continuously to destroy the other in pursuit of reputation and self-preservation; not all rational communities have self-interest as their only mode of behavior. It has been observed that even amidst harshest and toughest adversities, communities have cared for others and have stood for good moral values. This has been observed both within and between different countries. The recent anti-racist movement in United States and welcoming refugees from middle east into certain European countries are some of the examples of such behavior.

Game theory or other theories such as the one by Hobbes (a 16th century English philosopher) do not take into account the fact that most humans by nature, have social inclinations which include affection, friendship and building relationships. Community’s behavior in many occasions reflect these individual social inclinations. Also, the social behaviour that involves co-operation can be adopted and learned among communities such that social restrictions may not even be necessary to control individual behavior.

There are several advantages of co-operation among communities. For example, in the context of this pandemic, scientific collaboration would yield faster results in terms of finding better treatments, better control measures and accelerated development of vaccines, whereas economic collaboration in this time of crisis, can limit the impact of initial supply shock and temper down the dip in demand subsequently.

In the era of globalization, any pocket of epidemic can potentially bring back the pain and suffering for the entire world and it is a win-win for everybody if we think of world at large rather than our own communities or corporations.

Hopefully, the countries will judge their leaders on the basis of how they tackle this crisis, and in that case, optimal crisis management will be a bigger incentive in the payoff matrix for leaders. Keeping aside petty differences and egocentricity will become the most rational thing to do. In the tussle between morality and self-interest, hopefully during this humanitarian crisis of gigantic proportions, morality can be achieved through self-interest.

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