Dating Games
I’ve heard people describe dating as a game of chicken. And on the surface, the description seems to fit — you have two people who are approaching one another, and one of them might decide to back out at the last moment, leaving the other with a little less than what they might have expected.
But in game theory (and the actual game of chicken, as portrayed by Footloose in 1984), the game involves two cars, who — if they do not turn quickly enough — will end the game in a horrible crash.
That doesn’t seem quite like dating to me, so I’ve decided to dig a little deeper and try to find the correct description. Perhaps we’ll learn something interesting along the way.
Let’s start with game theory. What is it, exactly? Wikipedia describes game theory as “the study of mathematical models of strategic interaction between rational decision-makers”. This mentions that it is a model — so the intention is to illustrate a concept, and perhaps simplify a real-world interaction so that it is easier to understand. Strategic interaction to me means that there are two entities with consequences for their actions.
And finally, we expect all participants to be rational decision-makers… that already sounds less and less like any modern dating situation that I’ve heard of (insert sit-com laugh track here). This simply means that these entities act in their own best interest.
Consequences to actions and rational decision-making — these are both assumptions that we can use to simplify complex interactions between people who are in the dating scene.
If we dig a bit deeper, we’ll also find that game theory comes with nice, visual representations of these models, called payoff matrices. Each matrix illustrates a particular game, typically involving two players and a limited set of choices.
An example of a game is the prisoner’s dilemma. In this game, both players are prisoners in separate cells, and no means of communication, who can either choose to cooperate with each other (by staying quiet), or betray each other (by snitching on the other player for immunity).
The payoff matrix looks a bit like this: on the headings of the rows and columns are the possible choices each prisoner can make. The numbers within each cell represent the utility (or benefit) that each player receives for their choice, given the choice of the other player.
This illustration represents a set of payoffs that generally stay fixed, while players play the game repeatedly, over time. And like any game, people learn from previous decisions, and continually do so until they develop a strategy for their choices. In this particular game, you might have player A deciding to cooperate first, while player B cooperates as well. Then, on the second iteration of the game, player A might expect player B to cooperate, and subsequently choose to defect in order to improve their payoff. On a third iteration, we expect that player B will also choose to defect, in order to avoid a worse payoff.
Eventually, you expect both players to always defect. The expectations over time create a situation where neither player expects the other to cooperate, and an equilibrium will form, where the choices of both players no longer change. This is called a Nash Equilibrium (which we’ve highlighted in green).
You’ll notice a few things here. First — in some games, there is an optimal strategy, given a lack of knowledge about the other player’s choice. Secondly — the optimal choice does not always lead to the best payoff for either of the players. Let’s hope that this isn’t the case for dating.
If we return to the game of chicken — where two opposing players drive toward one another to see who turns first — we’d expect the model to have two different choices: continue (representing someone who keeps driving), or swerve (when someone turns).
The payoff matrix from the classic game of chicken should look like this:
If we use this as a metaphor for dating, we’d expect swerving to represent when one player decides stop dating the other player, and continuing to represent the choice to keep dating. Let’s take a look at the existing matrix for the game of chicken, and make some changes:
According to the payoff matrix above: if both people swerve the payoff is 0 for both players. That sounds about right — nothing really happens when two people decide not to interact.
If one person decides to continue while the other swerves, one player receives a negative payoff, while the other receives a positive payoff. Assuming that the average person doesn’t like to lead people on for fun (for simplicity’s sake), we should only expect that there are no positive payoffs here — since the players still won’t interact (though one player’s feelings might still get hurt).
Finally, if both people decide to continue, we should expect the only positive payoff in the whole matrix instead of the “crash” in the typical game of chicken. This is the situation where people enjoy dating one another, and continue to do so.
With all that, we should end up with a matrix like this:
You’ll notice that there are two Nash Equilibria. How does that happen? And what does it mean?
Let’s start with the first question, and figure out the how. Let’s imagine that you begin with players A and B both starting by swerving. Neither player has the incentive to switch their strategy, because they will end up with a negative payoff. In real life, an example of this is when two people ghost each other. Most people in this situation would expect that if they sent the other person a text, they’d be more likely to be ignored, given the other person is also deciding not to text them.
And if the game begins with one player swerving while the other continues, the one who continues is incentivized to swerve, so that they will not have a negative payoff. If you invited someone out for a drink and they ignored you, would you typically choose to invite them out again?
In the final case, if both players start by choosing to continue, they will stick to their path, as it is the outcome with the highest payoff for both players. This illustrates the case where you enjoy someone’s company, and you know that they like you too.
You’re probably thinking now that 75% of the time, we end up with a missed connection. In three of the four cases — both players swerving, one swerving and one continuing, or one continuing and one swerving — the model predicts that both players will choose not to interact with one another. If we pretend that you’ve gone through a whole texting and vetting process beforehand, 75% seems a bit high. Is this what dating looks like, in its simplest form? Are we stuck here? And what does all this mean?
In 2018, Neil Degrasse Tyson appeared on the Joe Rogan Experience, a podcast/talk show where Rogan interviews various guests. In his appearance, Tyson is asked about why he doesn’t have a phone case to protect his iPhone. Tyson takes out his nearly thousand-dollar phone and demonstrates how he holds it as he talks about his own method for protecting his phone.
People with cases tend to be less careful with their phones, because they expect the case to completely do the job. But most cases can only protect so much, and their phones end up damaged anyways. Tyson says that he chooses to modulate his risk instead, by being mindful of how he holds it and being mindful of the fragility of it.
We often forget the agency we have in our choices and the influence it can have on the situations surrounding us. Let’s look at what happens when we modulate our payoff matrix by removing the negative payoff for player A when player B swerves. In real life, this change would represent a decision to not take other people’s decisions too personally.
You’ll notice that the equilibria stay the same, but if you replay the possible steps in the game, you’ll also notice that there is now a 50% chance of reaching a positive payoff for both players.
In the case that you swerve, or both of you swerve, we expect the equilibrium to be the top right cell, but if they swerve and you continue, on the second round of the game, the other player is incentivized to continue as well.
Of course, this all assumes that there is a positive payoff for the other player — if they have no interest in you at all, or even dislike you, they will continue swerving. But without knowledge of this, it appears that your best strategy is to give people a second chance.
There were a lot of assumptions made in this whole analysis, namely the payoff values and the assumption that complicated situations can be simplified into four squares with numbers scattered within them. There is also the likely criticism that such deep analysis of emotional situations takes the romance out of them.
No single number can summarize all the desires and fears of a person, but perhaps — in quiet moments — when there is time to reflect, or when you feel like you’re overthinking, this reassurance that you are on the right path may calm your unsteady heart. And you’ll give people a second chance.
(Special thanks to my friends who shared their time, patience, and expertise during the editing process.)
