Considering Female Feticide in India from a Game Theory Perspective

India’s PCPNDT as a Socially Efficient, Mixed Strategy Solution

Young Indian women walk past a billboard in New Delhi encouraging the birth of girls on July 9, 2010. RAVEENDRAN/AFP/GETTY IMAGES

INDIA has been plagued by an antiquated and socially dysfunctional set norms around marriage and gender for centuries. Among them is the institution of Dowry, a practice where the bride’s family gives the groom money and gifts. As with many such norms, its intents and original purpose have a spurious relationship to its function today. It is in a sense, insurance for the bride in the case of widowhood or neglect — durable material assets that follow her into her marriage. In practice it’s a socially regressive, predatory custom. Grooms’ families have a lot of bargaining power and generally try and extract as many concessions as possible.

That dowry imposes huge costs on the bride’s family and equally massive benefits on the groom’s is sufficient to consider the problem at hand: the gender of a child bears large financial implications for the family. If we are to substitute “homo-economicus” — our traditional rational choice agents — into the situation faced by Indian families, what would we expect them to do? In our model there are no costs to sex-selection and no moral friction. Now we are necessarily considering the institution of dowry as fixed and exogenous to our model, our agents cannot do anything about it and must adhere to its rules. Seeing that even with national laws against dowry in place dowries have only increased and all but the most progressive Indian families engage in it, this diverges little from reality.[1]

That being the case, one would expect our agents in our model acting in a vacuum to maximize their chances of having a boy, to kill female children, or to have children until they have more boys than girls. In fact, this is all exactly what we see in real life India today. Since the 1990s, the most efficient means of sex-selection has been pre-natal screening, and the discrete abortion (which is illegal in India) of female fetuses. However — ethical qualms aside — when this behavior is aggregated, it is also not the socially efficient or utility maximizing outcome for our agents.

Before we begin constructing our scenarios, let us consider the problem of sex-ratios. It will become obvious that if all of our agents have boys, then there are no dowry payments or receipts, and everyone has an expected utility of zero (there are no LGBTQ folk in simulated India). Such a simplification creates neat decision matrices but doesn’t yield the type of problem actually faced by India today, so we have to make our agents care about more than just dowry. Some research and predictions suggest male skewed sex ratios can cause a great deal of dysfunction in societies for several, interrelated reasons. That research is budding, and complex. To account for the intuition that a male only society, or a single gendered society in general, wouldn’t lead to zero impact for our agents, let us say our agents care about both getting married as well as dowry. The following assumptions will suffice:

Everyone’s best case scenario is to have a son that marries, and everyone’s worst case is for there to be no marriage. For there to be marriage there must be men and women, which gives us an intuition to the coordination problem at hand. Everyone’s individually rational choice would clearly lead to socially inefficient outcomes. We can dramatize this via a matrix of a two-player game.

In this scenario, there are only two families in India who can each decide the gender of their child through whatever mechanism. Now, if either family were choosing gender ignorant or unconcerned with the fact that the other family could choose gender as well, they would treat the gender of the other family’s offspring as exogenous, a coin flip.

Both would choose to have a son; they would both have a utility of -100. However, if both families expect one another to behave strategically, then we run into problems; it ends up looking like the classic “Battle of the Sexes” (funnily enough). Uncoordinated, the agents cannot meet their optimal solution. If they both chose “Son,” they will both end up with no marriage and a utility of -100, a failure point. If they both individually flip a coin, they could do a bit better and have an expected utility of 0. However, if they both cooperate, they can choose between the two possible son/daughter pairings. The range of probabilities we can assign to which family has a son is our pareto optimal set of outcomes; neither can change their strategy along this range without making the other player worse off. Per John Nash’s account of the problem the negotiation point — or the Nash Point — that our agents would arrive at is to split the probability of having a son 50/50, since the outcomes are symmetrical. They would decide based on a coordinated coin flip.

This coordinated coin flip would decide who has a son. Guaranteed a marriage no matter what, each family’s expected utility would be 100. This is the solution that our rational agents in our two-family India scenario, given the chance to coordinate, would arrive at.

Does this logic translate to an n-family India scenario? Our agents are all better off if there was a 1:1 ratio of men to women in India, as everyone could at least have a positive utility. When accounting for the law of large numbers, in a country of say, 1.3 billion, a rule that required everyone to choose their child’s gender based on an individual coin flip would be just as socially optimal as the coordinated coin flip in our two person India.

In a sense, India has already adopted such a strategy. In 1994, the Parliament of India passed the Pre-Conception and Pre-Natal Diagnostic Techniques (PCPNDT) Act. This law criminalizes any deliberate sex selection process, with the explicit aim of arresting the declining sex ratio. In a sense, through social choice mechanisms outside the scope of this paper, Indians have attempted to adopt the mixed strategy that our agents in simulated-India have. Under the dowry system, everyone is better off flipping a coin on gender, even if choosing a son is the most individually rational.

However, this law — which is poorly enforced — really creates a different sort of game. When we consider this a situation where there is effectively no external penalty for non-compliance, we get a sort of modified prisoner’s dilemma or free rider problem.

The solution is unstable for a similar reason that cartels are (theoretically) unstable. Absent adequate enforcement, if everyone else complies there is a lot of gain from defection. If you’re complying and most people defect, you lose. This helps explain why, even with the Indian government’s concerted efforts, female feticide and discrete sex selection practices remain widespread.

[1] It’s interesting to consider that the level of dowry reflects the “market price” of a groom; the fact that those prices have gone up begs interesting questions about relative supply, demand and bargaining powers (elasticities in econ talk) of men and women.

PPE student, aspiring galaxy brain

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