Love & Marriage in the Times of KHADC Laws

Game Theory is the study of how we make decisions in strategic situations. Over the past few decades, it has gone from being a rarely used tool for economic analysis to being one of the most widely applied concepts, used in disciplines ranging from Computer Science, to the Social Sciences, and even to fields such as Evolutionary Biology. The versatility of Game Theory is such, that it has been used creatively, under a variety of circumstances, in situations of dilemma, to provide solutions to problems that were once thought of as unsolvable. The question of marriage, is one such situation.

Marriage is an important social institution, which has been closely linked to the mating patterns of primitive societies. Marriage is what determines the nature of familial relationships in a society. As such, it must be understood that it is not entirely a private affair, especially when viewed in the context of a country like India, where the family as an institution, has a say in the minutest of details, including the selection of a suitable partner. In fact, the question of marriage, has become such a sensitive topic, that even the state has taken it upon itself to be involved.

A particular example, is taken from Meghalaya, India, where a government organization (KHADC) has proposed a bill that seeks to redefine the identity of a woman who chooses to marry outside the community that she belongs to. Given such an interweaving of external factors and the question of love, we clearly see how Game Theory can help provide an answer.

Gary Becker, was one of the first researchers to apply modern economic analysis to the institution of marriage from a theoretical standpoint. Since Becker’s seminal work, several economists have studied marriage from a variety of standpoints. However, these studies have mainly focused on love marriages. Arranged marriages, continue to be in the dark, at least when it comes to academic discourse. In this regard, this note aims to add to the literature of game theory applications to love marriage vis-à-vis arranged marriage.

The Model

Consider a simple two-player, complete information game, played simultaneously in normal form, where the first player, labelled Descendant, represents an individual who makes the decision to either marry a partner of their choice (a love marriage), or to marry a partner chosen by their parents (an arranged marriage). The second player, labelled Parents, represents a benevolent, omniscient, and omnipresent social planner, whose main play, is to either ostracize or to withhold from ostracizing, individuals based on their choice of a partner. We assume that the players are rational and self-interested, i.e., the objective of each player is to maximize their payoffs, ui given the strategy played by the other player. We also further assume that Parents would prefer their Descendants to marry a partner of their choice.

Let i represent the player, where i = Descendant (D), Parents (P).

Let Si represent the strategy space, where SD = {Arranged Marriage, Love Marriage} and SP = {Ostracize, Don’t Ostracize}.

For simplicity, let us assume that for Player D, the utility derived from marrying a partner of their own choice is x, where x > 0; while the utility derived from marrying a partner of P’s choice is the negative of x. For Player P, the utility derived from D marrying a partner of P’s choice is y, where y > 0; while the utility derived from D marrying a partner of their own choice is the negative of y. For ease, we assume that the cost of ostracism for both players D and P, is given by c, where c > 0; while the benefit to P of ostracizing D, is given by b; where b > 0.

We consider two variants of the game, one where there are costs to both the players from ostracism, i.e., costs to D, from being ostracized by the parents, and costs to P, from ostracizing a descendant of the unit; as well as a variant where there are costs to both players, and benefits to P specifically, from ostracizing D. These benefits, may be considered as the gains from maintaining cohesion within the unit by eliminating potential sources of conflict. The payoff matrices for each game are given, where the payoffs are written as (uD, uP).

Analysis

First, we consider the variant of the game where there are costs incurred by both players from ostracism. The general form of the game is shown below as Figure 1. A simplified example using assumed values for the variables is also presented.

We consider Player D, whose payoffs are listed first in each cell. Given that Player P plays Ostracize, the best response of Player D would be to play Love Marriage, since x – c > – x – c. If Player P plays Don’t Ostracize, then again, the best response of Player D would be to play Love Marriage, since x > – x. Clearly, it would appear that Love Marriage is a dominant strategy for Player D.

Now, we consider Player P, whose payoffs are listed second in each cell. Given that Player D plays Arranged Marriage, the best response of Player P would be to play Don’t Ostracize, since y > y – c. If Player D plays Love Marriage, then again, the best response of Player D would be to play Don’t Ostracize, since – y > – y – c. Clearly, it would appear that Don’t Ostracize is a dominant strategy for Player P.

Given the best responses of both the players, we see that the Pure Strategy Nash Equilibrium (PSNE) for the game is given by (Love Marriage, Don’t Ostracize), with corresponding payoff vector (x, – y). An outcome such as (Arranged Marriage, Ostracize) with payoff vector (– x – c, y – c), would never be reached in such a setting. The best response payoffs have been underlined in Figure 1.

An interesting point to note, is that the payoff realized by Player P in the PSNE is negative i.e., – y. A simple justification for this, comes from the fact that parents are altruistic, and at the end of day, should have their descendants’ best interests at heart.

We now consider the second variant of the game, which introduces a benefit to Player P, from ostracizing Player D. We will then consider two cases of the game, one where b < c, and another where b > c. The general form of the game is shown below as Figure 2.

It must be noted that benefit, b appears as a cost, in the case where the outcome reached is (Arranged Marriage, Ostracize), as it would prove to be counterproductive for Player P, to ostracize descendants who marry a partner of their parents’ choice.

Case A: b < c.

Figure 2a represents the first case, as shown below.

 

Clearly, this version of the game yields the same result as the first version of the game considered. Given the best responses of both the players, we see that the PSNE for the game is given by (Love Marriage, Don’t Ostracize), with the corresponding payoff vector (x, – y). Again, the best response payoffs have been underlined in Figure 2A.

Case B: b > c.

Figure 2b represents the first case, as shown below.

In this variant of the game however, we do see some significant changes. Considering Player D, we see that nothing changes, with Love Marriage remaining a dominant strategy as in the previous cases.

However, when we consider Player P, we see that when Player D plays Love Marriage, it is no longer a dominant strategy for Player P to play Don’t Ostracize, i.e., given that – y – c + b > – y, the best response for Player P would be to play Ostracize.

Given the best responses of both the players, we see that the PSNE for the game is no longer given by (Love Marriage, Don’t Ostracize), but is given by (Love Marriage, Ostracize), with corresponding payoff vector (x – c, – y – c + b).

Conclusion

As can be seen from the preceding analysis, any attempts by a paternalistic social planner in this case KHADC, to seek retribution on individuals who choose to marry partners of their own choice, so as to influence them to marry suitable partners according to its opinion, will fail to produce the intended outcome. Rather, such a policy would be self-defeating, and would produce an outcome where all individuals would choose to marry partners of their own choice, and bear the brunt of being ostracized. This is detrimental to any society, as it would eventually lead to its disintegration, and finally, extinction. A social planner, should not be in the business of affirming or enforcing love. Consenting adults are free to make choices about their relationships without having to redefine marriage, and should not require approval to do so.

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Everything in the universe can be broken down into a cause, and an effect of that cause. Causality is the glue that links the two phenomena, and econometrics is the art that makes sense of this relationship. Daniel is currently a second-year master’s student at the University of Delhi. He considers himself an empiricist, motivated by a consideration of proving theorists wrong. His primary research interests are in the fields of discrimination and identity, and economic development. He plans to take his interests further by pursuing a PhD in the near future.

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Daniel Ebor Challam Written by:

Everything in the universe can be broken down into a cause, and an effect of that cause. Causality is the glue that links the two phenomena, and econometrics is the art that makes sense of this relationship. Daniel is currently a second-year master’s student at the University of Delhi. He considers himself an empiricist, motivated by a consideration of proving theorists wrong. His primary research interests are in the fields of discrimination and identity, and economic development. He plans to take his interests further by pursuing a PhD in the near future.

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