Understanding #MeToo as a game
By: Naman Jain
Tags: Economics, Metoo, Discrimination, Sexual Assault, Game Theory

The #MeToo campaign has rapidly gained momentum following the Harvey Weinstein case, and has spread like wild-fire around the world, including India. While a lot of women have come out with their scarring experiences, many have passed this as a farce, and opposed it with furor,men and women alike. It can be extremely difficult to comprehend why a woman would be willing to tell her story after months, or even years, when she did not object to it while being harassed in the first place. Game theory may resolve this conundrum.

It is crucial to understand this silence, and why this movement is important to prevent such horrendous crimes in future. First, to understand why women or , in fact, anyone who is molested or sexually assaulted, does not want to report the crime. The obvious answer that comes to our mind is that they are scared of the consequences. It is too big a risk for them to report since they fear the societal, psychological and practical consequences of reporting. However, there are more insidious reasons as well. In many cases, the perpetrator is often a person with power, or their senior at work, or even someone too close to them, like a relative.

The victim is often shunned by people they trust if they open up, and many a times they are confused about if what happened with them even constituted to harassment. After all, harassment can be misconstrued as a playful gesture, or harmless by the perpetrator. And this is just the tip of the iceberg, with a plethora of reasons at play. In economic terms, it is just too “costly” to report or open up.

For the sake of explanation, let’s say there are 2 parties in the game: perpetrator (P) and victim number 1 (V1). Assuming that both the parties are rational, and P has the intention of harassing, while V1 is a latent individual who can not stop the harassment. The actions available to them are:

P can either harass or not harass

V can either report or not report

Now, formulating this as a game yields interesting results. In the current time period, the game looks somewhat like this:

We use a concept called as backward induction to solve this game. In the event, when the perpetrator harasses, the payoffs available to the victim when she reports and not reports are -10 and -5 respectively. This is formulated in such a way assuming that the costs of reporting as mentioned above are too high for the individual to report. Clearly, the victim will choose to not report the harassment in this case and the perpetrator ends up getting a payoff of 5.

In the event that the perpetrator does not harass, the victim is assumed to be indifferent between reporting and not reporting. (A caveat here is that in this case, as some may argue, it may be in the favor of the victim to report as they can gain more utility by falsely reporting the crime. However, I’d disregard that case for simplicity). Since the victim is indifferent between reporting and not reporting, we can assume she randomizes with equal probability, and thus the expected payoff to the perpetrator turns out to be -2.5. The Nash equilibrium of this game is when the perpetrator harasses and the victim does not report and both get the payoff of 5 and -5.

Moving forward, the victim carries psychological costs of harassment with her throughout the rest of her life, and has an option to report the crime in future, which can increase her payoff by the way of redemption, but will reduce the perpetrators payoff. The negative psychological payoff of not reporting is discounted every year, meaning that the negative payoff falls year after year. But the total lifetime payoff of the victim from reporting is still not greater than not reporting.

Mathematically,

V1’s payoff from reporting: -10 + (-10)δ + (-10)δ^2 + (-10)δ^3 + …

V1’s payoff from not reporting: -5 + (-5)δ + (-5)δ^2 + (-5)δ^3 + …

The geometric progression can be solved to yield the total payoff from not reporting which comes out to be -5(1/1-δ). For simplicity, we can assume this discounting factor to be equal to 1/2, thus making the payoff from not reporting (-5*2 = -10) to be greater than that of reporting (-10*2 = -20). Also, note that there is some positive payoff from reporting available to the victim at any period of time, but this is not big enough to still shift the decision to reporting. (It can be anything between 0 to 10, say 5 again). So from reporting the victim can at most get -15.

Now, after some time, the perpetrator harasses someone else (V2). However, this victim does not have high social costs of reporting and she reports the perpetrator. This can be seen as the rise of the #MeToo campaign, where someone raises their voice against harassment. This has a twofold impact: It reduces the payoff of the perpetrator, and it also reduces the social costs of reporting for the victim (V1). The social costs, which were -10 earlier now can reduce. This would mean that at that period, it now makes sense for the victim to actually report the crime and further impact the payoff of the perpetrator.

This is a very simplified game, and can be made more realistic by adding uncertainties about the different types of perpetrators and victims. However, this simple game is powerful enough to provide a logical explanation for an important phenomena like the #MeToo campaign. The same argument can be extended to other movements around the world like the #BlackLivesMatter, #ELSIceBucketChallenge and the like.

What is even more important is to understand how this movement impacts the future behavior of the perpetrator and how lasting the impact will be. But that is not the motivation behind this article, and is left for the readers to explore.