The Economics of Love

When I saw that my next blog post was going to post on Valentine’s Day, I asked myself the question: “What can economics tell us about love?” I know, I know, the two seem like polar opposites, and most people would probably not describe economists as natural romantics. But economics and especially my research area of game theory have a lot to do with how people respond to incentives and strategically interact with each other. There’s actually quite a bit economics can tell us about love.

The Gift-Giving Dilemma

In 2021, Valentine’s Day spending was estimated to total $21.8 billion or roughly $165 per person. It is just a myth that greeting card and candy companies invented Valentine’s Day to make us buy their products. Still, couples every year find themselves in the dilemma of gift giving.

Picture this: A married couple wants to treat each other to Valentine’s Day gifts, but household finances are a little tight right after the holidays, and they are considering agreeing on a spending limit for gifts. For now, let’s assume they both care about the gift that they receive and their household budget.

If both partners (let’s call them Romeo and Juliet) stick to the spending limit, they don’t get the greatest gifts, but they feel financially responsible, and the household budget remains intact. Let’s say that gives each of them a level of happiness that we’ll call 2. Now of course either of them can deviate from the agreement and splurge on a gift for the other.

Splurge Or Not?

If only one of them splurges, things are still all right financially. The person who gets the great gift has a level of happiness of 3, while the other person is left with a relatively boring gift and has a level of happiness of 0. If both of them splurge, they are both very happy with their presents. The household budget took a hit, though, and therefore they each end up with a happiness level of 1. This is lower than when they both stay on budget.

We can represent this situation in the following payoff matrix in Figure 1, which will help us to determine what outcome we should expect in this situation. Romeo and Juliet each have two strategies they can choose from – stick to the agreed budget or splurge. The first payoff number in each cell denotes Juliet’s happiness, the second payoff number in each cell is Romeo’s happiness. So, for example, if Juliet sticks to the budget while Romeo splurges, Juliet gets a payoff of 3, while Romeo gets a payoff of 0.

By The Numbers

Now what do we expect Romeo and Juliet to do in this situation? If Juliet thinks that Romeo is going stick to the budget, then she gets a payoff of 2 if she also sticks to the budget. She gets a payoff of 0 if she does not. Therefore she’ll want to stick to the budget in this case.

If she thinks Romeo is going to splurge, then she will get a payoff of 3 if she sticks to the budget. Conversely, she’ll get a payoff of 1 if she splurges as well. Therefore she will once again choose to stick to the budget. Hence, regardless of what she believes Romeo will do, sticking to the budget is her preferred (or “dominant”) strategy.

We can repeat the analysis for Romeo and we’ll find exactly the same thing: he will want to stick to the budget regardless of what Juliet is doing. Therefore, the predicted outcome of this situation is that they both stick to the budget, and they both get a payoff of 2.

True Love Mapping

Now remember that we assumed that both of them care mostly about the gift they receive when we defined our payoffs. When you’re in love though and buying presents for one another, you may actually care more about making the other person happy than you care about the gift you get.

This has also been called the “True love mapping”. The true love mapping essentially switches the players’ payoffs. For example, if Juliet splurges and Romeo does not, Juliet is overjoyed that she can give Romeo an awesome gift that he’ll love. She now gets a happiness payoff of 3. Romeo however now feels badly that Juliet only gets a boring gift and his payoff is now 0.

So contrary to the previous situation, when two people are in love, the other person’s happiness is what matters most to you. As a result, what kind of gift you give to your partner becomes more important than what kind of gift you receive.

Changing Outcomes

So how does true love change the outcome of our gift giving game? Let’s write down the new payoff matrix by switching Romeo and Juliet’s payoffs for all possible outcomes.

Now, Juliet has a higher payoff if she splurges regardless of what Romeo does (3 vs. 2 and 1 vs. 0) and likewise for Romeo. Therefore, if both partners care more about the other’s happiness than their own, we will end up in a situation where they both splurge on a gift and they blow the household budget.

Each of their payoffs is 1 in this case, which is actually lower than their payoff in the original scenario when they acted out of self-interest and not true love! The lesson from economics here thus is that love may make us do crazy things that may end up making everyone worse off.

A Win for True Love

Ok, so maybe true love doesn’t always lead to better outcomes, but there certainly have to be situations where true love saves the day. As it turns out – there are! This next example will illustrate how true love (and caring more about others than ourselves) can help us overcome coordination problems.

Consider the following situation: Bonnie and Clyde have committed a crime and are running from the police. Eventually, they get caught and are put in separate rooms at the local jail to be interviewed.

For now, we’ll suppose Bonnie and Clyde both want to spend as little time in jail as possible. If Bonnie and Clyde both refuse to confess to the crime, they can only be convicted of a lesser offense which carries a sentence of one year in jail. If both of them confess, then they both get sentenced to two years for the major crime. However, the police offer them a deal: if one of them confesses while the other denies, the person who confesses goes free and the other one will get a sentence of three years.

True Confessions

Let’s see what this looks like in a payoff matrix. We will say that each year in prison amounts to a negative payoff of -1, so a two year sentence is a payoff of -2, etc. Bonnie’s payoffs are the numbers listed first, Clyde’s payoffs are the numbers listed second.

This is an example of the classical Prisoner’s Dilemma. Even though the best joint outcome for Bonnie and Clyde is to deny everything and each only get one year in jail, confessing is the dominant strategy for both players. To see this, put yourself in Bonnie’s shoes: If she thinks Clyde is going to confess, she is looking at 2 years in prison if she also confesses, but 3 years if she denies.

If she thinks Clyde is going to deny, then she can walk free by confessing vs. one year in jail by denying. Again, confessing is the better choice for her. The same logic applies to Clyde, and therefore we’d expect both of them to confess. This is an example where self-interested individuals could be better off by coordinating and denying. But the coordination breaks down because no one wants to risk the harsher punishment in case the other person caves and confesses.

What About Love?

Enter true love. If Bonnie and Clyde are madly in love, they may care mostly about saving the other from a lengthy jail sentence. As in the previous example, we can model that by simply switching their payoffs. That is, if Bonnie confesses while Clyde denies, Bonnie feels so terrible about having sent Clyde to jail that she gets the payoff of -3. ButClyde is happy to have set Bonnie free and gets a payoff of 0.

Here is what the transformed payoff matrix looks like.

Under true love, both Bonnie and Clyde now always want to choose “Deny” and reach the joint optimal outcome! Therefore, true love can overcome prisoner’s dilemma type situations and enable coordination.

The Crux of Online Dating

A different aspect of “true love” becomes evident when you sign up for online dating. The internet has made it easier to find and connect with other single people. But it has also made it harder to figure out if someone is seriously interested or simply sending messages to everyone hoping to score a date.

Before online dating, the “cost” of asking someone out for a date was somewhat higher. You first had to coincidentally meet a person, figure out if they are single, and then you had to muster up the courage to ask them out on a date. Online dating has significantly reduced this “search cost”, as you can view profiles of available prospects with the click of a button in your dating app.

Swipe Right For A Job

A similar problem has arisen in the labor market, where online recruiting has reduced the cost of applying for jobs. In the past, job seekers were more selective when sending out applications, as there was a monetary cost associated with each packet they printed and mailed out.

As things have moved online, the marginal cost of sending out another application is close to 0 (as an economist I say close to 0 to account for the cost of your time). As the applicant, this is great news! You can apply for jobs that are long shots or jobs that are really just a safety option without having to spend a fortune.

As the hiring company, though, you are now faced with a different problem. You will likely receive a lot more applications for each job posting, but how do you know which candidates are actually worth pursuing? You’d hate to waste your time and limited resources trying to hire someone who is out of your reach and really hoping for a different job offer.

A Rose By Any Other Name

The same holds true for online dating – since the “cost” is so low, why not ask everybody who you are remotely interested in for a date? However, as the recipient of these invitations, how can you tell the difference between offers to go on a date that are genuine, and offers where you are the consolation prize?

This is where economics can help us out. The idea is the following: Wouldn’t it be nice if the person inviting somebody on a date had a way of letting the other person know that they are seriously interested and not just sending a note to everyone? Of course we could write a heartfelt message swearing that the recipient is the man/woman of our dreams. But talk is cheap (this is actually what we call “cheap talk games” in economics), and likely won’t convince the experienced online dater.

What we need instead is a credible signal that we can send to show our interest. Economics tells us, that for a signal to be credible, it needs to be costly. The cost associated with sending it will deter those who are not serious. An online dating site in Korea tried the following to solve the credibility problem: Each person on the website got two virtual roses that they could send to someone with a request for a date.

Given that roses were limited to two, sending a rose is a costly signal and can thus credibly convey sincere interest. Researchers who analyzed data from this Korean dating website found that sending a virtual rose did indeed increase a person’s chances of having an offer for a date accepted.

Happy Valentine’s Day!

I hope you enjoyed my little examples that show that economics and love aren’t polar opposites, but that models from economics can help us understand human behavior a little bit better and can help us reach more desirable outcomes.

If you are interested in learning more about game theory, become a Buff and take courses such as microeconomics or industrial organization where we talk about strategic interaction like this!

Anne-Christine Barthel
Assistant Professor of Economics and Decision Management