True Love is a Nash Equilibrium

Why your love maybe more transactional than you think

I. Love in the Time of Popular Psychology

It seems like pop-psych practitioners are baffled by love these days. 

Someone is out there ready to find flaws in every relationship (except Ryan Reynolds and Blake Lively’s maybe). Pop-psych guys are offended by dominating partners and disturbed by submissive ones. They find couples either too dramatic or extremely boring. One will describe your choice to take your partner’s surname as archaic. But if you’re a man, they will celebrate that choice. One will lambast your decision to move countries for your partner. If you decide to not move, another will wonder if you have what it takes to make long distance work. One over-values the role of sex in a relationship, another is dismissive of it. One will find your decision to stay monogamous old-fashioned. Another will find your decision to be polyamorous too progressive. Most are disgusted when you don’t leave your cheating partner. And they are suspicious when an ex suddenly appears in the picture. Also, you cannot be a homemaker without inviting judgement. Neither can you break the glass ceiling without having relationship troubles. You are either too similar to your partner or eerily different. Your partnership is collaborative to some of them some of the times, and other times, they label it as codependent. They cancel your marriage if it falls outside their political ingroups. They pity partners who don’t recognise mansplaining. They barely hold themselves back from saying I-told-you-so after you’ve been love-bombed. After all, they had warned you of the dangers of being ghosted and breadcrumbed.

There used to be a time when love had a uniform definition, and a fixed sequence. You both will get butterflies in your stomach when you first see each other. You will declare your love for and to each other. You will get married and move into a house together. You will have children and raise them. If you are a woman, you will have to bear more of the household responsibilities. The success of your marriage will be contingent on your willingness to sacrifice and compromise. There will be challenges, the love may fade over time. One or both people may cheat. Your children will move out. You’ll then grow old together and eventually die. You would have lived a good life. In this Olden age, there was a much clearer idea of what was right and wrong in love. 

It’s 2023 and the relationship landscape has changed a lot. Being in a relationship today cannot confirm anything to an outsider - it could mean that you are married or unmarried, it could mean that your relationship is closed or open, it could mean that you’re a raising a plant, pet or a child with or without your partner, it could mean that you live by yourself or with your partner, it could also mean that you live with your partner and their parents or with them and your parents. Everything is so uncertain. And so, coupled with nudges from popular psychology and popular culture in general, we give out all kinds of scrambled signals about what is okay and not okay in love. Sometimes, our own relationships reflect what we promote as love. Other times, our own relationships reflect the flaws that we point out in our neighbouring relationships.

This raises a question, one that people have spent whole lifetimes searching for an answer: What is true love?

Bill and Melinda Gates stayed together for 27 years and raised 3 children before filing for divorce. This is in stark contrast to couples who break up after just a year of being together. I often hear stories of women who are in abusive relationships yet cannot picture a life without their partner. Having grown up in the Gulf, I’ve seen many couples who have lived pretty much all of their lives away from each other meeting only for vacations and after retirement. I continue to see people religiously guard against cheating, but I also see open relationships being discussed more frequently today than ever before.

I’m not sure if most of us know what we mean or understand by true love. We shift our definition of love based on the direction the tides of the cultures we are part of and the groups we hang with, take us. 

II. What psychologists have to say so far on the issue of love

Psychologists, across time, have theorised on what underlies the experience of love. Dr. Robert Sternberg, for instance, framed the experience of love as three-pronged. Love, according to Sternberg, is composed of passion, intimacy and commitment. Passion here speaks to physical attraction, intimacy to emotional connection and commitment to cognitive perseverance. Depending on how these 3 components combine or not, it can pave ways for different kinds of love. Relationships where intimacy is present, for example, but passion and commitment are lacking are described as friendships by this theory. Fatuous love, on the other hand, will see both passion and commitment present but miss the much needed foundation of intimacy. Infatuation, on the other hand, will have only passion.

According to Sternberg, only relationships that include all three convert into a successful, satisfactory partnership. He calls this kind of love Consummate Love, the kind that partners in long-term romantic relationships or marriages strive to attain, but rarely succeed at.

Another well known theory about love is the Attachment Theory of Love first proposed by John Bowlby. This theory suggests that how you love as an adult depends very much on how you were loved as a child. If your relationship with your parents saw all your needs met and was devoid of abandonment fears, it’s likely that you will be a secure partner. On the other hand, if you grew up feeling uncared for and neglected, you may become a romantic partner who is anxious or has avoidant tendencies.

There are a few other theories of love as well that I stumbled upon in my research but none of these theories (including the ones above) are backed by strong evidence. They still sound plausible and you will every now and then come across their personifications, I don’t disagree with that.

Notwithstanding all these explanations, there still is so much confusion in the general public’s understanding of what constitutes true love. For example, many relationships that are often described as successful are marked by a complete absence of love or intimacy. Many couples have very little to hold onto in their marriage except for their joint societal status, mostly owing to their career choices or life achievements. Yet their union is admired, people look up to their relationship as aspirational. Contrast that with a couple who lived many decades in a fulfilling, intimate marriage before deciding to part ways. It doesn’t matter how high the quality of their marriage was, once divorced, their marriage is moved to the department of relationship failures. 

If a couple adopts children without getting married at all, they are more likely to collect lots of disapproval or lots of astonishment or lots of both. How about a couple where one partner is battling alcohol addiction with little success? Some may view the decision of their spouse to stay with them as a sign of true love. Others may think of the sober spouse as stupid for putting their family and kids at continued risk. 

I have seen only one exception to people’s chaotic, shape-shifting understanding of love in all the time that I have been alive (I’m not that old by the way, so I could be wrong here). A relatively stable trait that people associate with true, successful love is longevity. It doesn’t matter whether you are open or monogamous, with children or without, staying with in-laws or not, in love or in hate, fighting or are diplomatic, good-looking or not, with your husband’s surname or your father’s - as long as you don’t split up, you are, to most of society, a successful and in-love couple. Even if people find it difficult to comprehend your relationship, they will still give you credit for surviving the biggest threat to a romantic relationship - time. If you are one of those couples who have stood the test of time, people may wonder out loud or in secret how you did it or are doing it. 

What is the secret to a successful, ever after love? Enter The Unpopular Theory of Love (TUTL).

III. Unpopular Psychology’s Theory of Love 

Unpopular Psychology’s Theory of Love is unpopular because it approaches love as more transactional and ascribes relatively little value to intimacy or attraction.

According to TUTL, love happens at Nash equilibrium, and love is sustained by Nash equilibrium.

A complex, more robotic definition of TUTL: True love occurs for the first time when two (or more) individuals reach a Nash equilibrium and is sustained as long as all parties continue to be in at least one of many possible states of Nash equilibria within the confines of the said relationship. 

I know this sounds like a bunch of made-up, scientific-sounding BS. So I must explain.

First, what is Nash equilibrium? Nash equilibrium is a concept in game theory. It is a state in which no single player in a game can gain any additional benefit by changing their strategy, as long as the other players don't change theirs.

An easy way to understand Nash equilibrium is this - think of a game being drawn. The game is drawn because no individual player can gain an advantage by making a different choice. It is an outcome that is considered optimal, a win-win situation.

A non-love example of Nash equilibrium:

Imagine that you and your colleague are each promised a bonus if you complete an optional assignment over the weekend. Added context to this is that your workload has already been a lot this past month and you are seriously contemplating if the bonus is worth giving your weekend up for. You know that your colleague is also grappling with a similar decision.

There are 4 possible outcomes to this situation:

1. You do the assignment; your colleague does the assignment; outcome 1: both of you get the bonus

2. You do the assignment; your colleague does NOT do the assignment; outcome 2: only you get the bonus

3. You do NOT do the assignment; your colleague does the assignment; outcome 3: only your colleague gets the bonus

4. You do NOT do the assignment; your colleague does NOT do the assignment; outcome 4: both of you don’t get the bonus

Naturally, Outcome 1 where both of you get the bonus is the optimal outcome in this case. That’s the Nash equilibrium. 

How does this concept apply to true love?

A couple I know were together for 8 years before calling it quits. From the outside, they seemed to have contrasting personalities. They constantly fought and often quite publicly. There were a few incidents when their fights even got physical. The intensity of their conflict was also reflected in the intensity of their affection. They were known for their elaborate and public displays of affection. Each of them would often separately confide in their friends that they feel unsure about the long-term prospects of the relationship. What made this chaotic, uncertain love last for 8 years? And why did it suddenly end after 8 years?

TUTL makes it very clear. For those 8 years, no matter how difficult and undesirable their relationship seemed like on the outside, both the partners were in Nash equilibrium. Being together was the best possible outcome out of all the possible outcomes that seemed available to them. It could have been that they did not have other mate choices available to them during that period. It could have been that they both had similar backgrounds which made them feel like a third person might not get why they think and behave in the ways that they do. It could also have been that they found it easy to be vulnerable to each other. It could have been that one of them had a lot of money and the other was physically very attractive and that seemed like a fair trade to make. It could have been that one of them was extroverted and personable while the other was introverted and intelligent which made each value their partner’s personality traits more than their own. It could be that one or both of them experienced abuse when they were young and so the fights felt like familiar, comfortable territory (Freud called this repetition compulsion). It could have been something else altogether as well. My point is that nobody forced them to be in what seemed to be a clearly unhealthy relationship. They stuck around because they both thought that they were getting the better end of the deal, even though it may not have seemed that way to the witnesses of their relationship. 

So what happened after 8 years? Why did they decide to break up then? If you’ve understood TUTL and Nash equilibrium by now, you’d have guessed that a better choice must have been made available to one or both of them. You guessed right.

What happened in reality, as far as I know, was that one of the now ex-partners met someone on a trip and decided to explore a relationship with that person. The previous Nash equilibrium was broken. So that relationship naturally ended.

If you view so many of the relationship tropes out there through the lens of Nash equilibrium, you’ll understand them suddenly very differently. I’m talking about gold-diggers, friends-with-benefits, soulmates, childhood sweethearts, opposites attract, love at first sight.

IV. Umm okay, so what’s the connection between true love and Nash equilibrium again? 

True love first happens when you arrive at Nash equilibrium with another person. He was tall and she was pretty - bam, Nash equilibrium! But then he started talking - Nash equilibrium broken. I would argue that even arranged marriages for which India is both famous and infamous for is based on the same principle. She came first in the IAS exam, he came second - who else can they marry but each other?

It’s possible that being in a state of Nash equilibrium is what aids much of the intimacy, passion and commitment that Sternberg talks about. When you think you’ve made the best choice of all the choices available, it makes total sense that you will experience strong feelings of attraction and love towards your partner. This may also explain why many relationships, despite poor intimacy or weak commitment, go on for years. 

What is important to catch here is that Nash equilibrium is not only necessary for the occurrence of love, it is needed for the sustenance of it as well. When a couple celebrates their Platinum jubilee, what this means according to TUTL is that, together, they have managed to sustain the conditions that kept both of them in a Nash equilibrium for 70 long years. It is certainly a feat worth celebrating.

At the end of the day, true love, as unromantic as that sounds, is a trade. We trade loneliness for companionship, agreement for affection, surnames for acceptance, and individuality for contentment. There will be negotiations. There will be boundary conditions. And that is not necessarily a bad thing. What is important is that both parties feel that their relationship is valuable inspite of the tradeoffs. TUTL posits that this is the secret of true and successful love. The best of relationships often feel like you’re in a sustained state of Nash equilibrium i.e., at any point, no partner has an incentive to deviate from their choice to be in the relationship, assuming that the other partner’s intentions remain largely unchanged.

V.  Why did you have to tell me about TUTL? What am I supposed to do with this knowledge?

The applicability of TUTL stretches far and wide.

Application #1: If you think that you are stuck in a relationship that is no longer adding any value to your life, TUTL encourages you to revive the Nash equilibrium in your relationship. Reflect on the conditions that got you into the relationship in the first place, and think about whether they continue to remain true. For example, if your partner’s caring nature is what initially drew you to them and lately you’ve been feeling neglected, initiate that conversation with your partner. Tell them that you are feeling neglected (subtext: I’m no longer gaining the value that I was promised out of this relationship). Also reflect on the role that you can play to restore the broken equilibrium.

Application #2: If you are deciding whether you’re ready to commit to somebody you’ve been seeing for a few months, TUTL could help you make that decision. Ask yourself what your expectations of a committed relationship are. See if this person will be able to meet those. Ask them too what their non-negotiables are should they choose to enter a committed relationship. Reflect on if you feel capable of meeting their desires. Maybe there will be room for some compromises, explore that. TUTL helps you make these decisions more rationally than push you to blindly walk into what you think is love but in reality is a potful of regret in cooking.

Application #3: Couples' therapy too, if you think about it, has actually quite a few roots in TUTL. Couples often end up going to therapy because of an implicit or explicit recognition that they are no longer in any kind of equilibrium, that the partnership is not feeling like a valuable one to go on with. A strategy commonly employed by the therapist in these cases is to make the couple resettle into their old equilibrium. They ask the couple about memories from the first few years of the relationship, task them with writing love letters to each other, and advise them to rekindle old love again. In other cases, therapists encourage their clients to find a new state of equilibrium. The therapist here, for example, may ask - How have you both changed? (subtext: Are there new things that you can value in each other, that can convince you to stay together?) Sometimes they succeed in regaining that balance, other times they don’t. TUTL is just a good aid to help them make the decision.

VI. Is love as dreary and uninteresting as you are making it out to be, Anju? 

My intention by writing this post was not to downplay the experience of love at all. I was frankly aiming to do the opposite. TUTL shows that love is not necessarily a mysterious, inexplicable phenomenon that is only meant for a few lucky individuals. It is actually a coming together of two individuals who find immense value in each other’s presence so much so that they start living together, travel together, attend parties together, watch movies together, get bored together, raise children together and stubbornly insist on being buried next to each other. What could be more beautiful than that?

TUTL is perhaps the greatest assurance that we all can and will find love. Somebody out there is seeking exactly what you have to offer to a relationship. It is also reassuring for those of you who are in love. The world may judge your relationship and call it too regressive or too progressive or too toxic or too dramatic or too boring and the thousand other unpleasant relationship adjectives that are out there but TUTL says that if your relationship works for you, then it works for you. And that’s enough. Unless you are in an abusive relationship. If you’re in an abusive relationship, you must know that no matter how implausible it seems like, you are not in any kind of Nash equilibrium with your partner. It doesn’t matter what value you think your partner is adding to your life, abuse nullifies it all. A TUTL practitioner would recommend that you exit that relationship immediately.

Those of you who are familiar with or have engaged with game theory might be tempted to argue that game theory assumes that all players are rational and hence make only rational decisions. You may want to contend that people are highly emotional when in love and therefore lovers cannot be considered rational, and so game theory can’t be applied in love. I disagree. I think humans often use love, among other emotions to mask the logic behind their decisions especially when that logic is not pretty-sounding (who wants to hear that they were proposed to for their earning potential?). A lot of the time, we know exactly what we are doing, even if we don’t admit it to ourselves.

John Nash was awarded the Nobel prize in 1994 for his work on the eponymous Nash equilibrium theory. In the movie Beautiful Mind that is based on his life, Nash credits love in his Nobel-acceptance speech. He is shown to say, “I've always believed in numbers and the equations and logics that lead to reason. But after a lifetime of such pursuits, I ask: 'What truly is logic?' 'Who decides reason?' My quest has taken me through the physical, the metaphysical, the delusional -- and back. And I have made the most important discovery of my career, the most important discovery of my life: It is only in the mysterious equations of love that any logic or reasons can be found.”

His own life however veers far away from the truth of these purported lines. His relationship with his first wife, ex-wife, and second wife (all of which are the same person) only further demonstrates the applicability of the Nash equilibrium in love. It later turned out that he never actually said these lines in his acceptance speech. The directors of the movie used their creative licence to put these words in his mouth. I’m not surprised that he didn’t say anything of the sort. If you ask me, if at all he would have said anything about love, I think he’s more likely to have said,”… And I have made the most important discovery of my career, the most important discovery of my life: Even in the mysterious equations of love, logic and reason can be found.”

P.S. If you enjoyed reading this post, here are 4 ways to thank me:

I will keep this post published regardless of your choice, looks like we hit a Nash equilibrium here :P