In the basic prisoner’s dilemma, the optimal strategy is to defect since the cooperation of the other actor cannot be guaranteed. Each actor’s payoff will be better by defecting regardless of the choice of the other player. Since Player A cannot guarantee the cooperation of Player B she will choose the best course of action for herself regardless of B’s choice.

For the purposes of this model, we can assume Carly Rae Jepsen is a rational actor. She begins the song with the words “I threw a wish in a well / don’t ask me I’ll never tell.” This indicates a clear set of preferences. The fact that she will not reveal her wish under any circumstances indicates that these preferences are constant throughout the game. Carly also sets up a ranked order of preferences, noting “I’d trade my soul for a wish / pennies and dimes for a kiss.” This monetization of kisses indicates her ranking is in fact quite sophisticated.

However, assuming the boy is a rational actor as well (which Carly does) the prisoner’s dilemma would predict that her optimal strategy is to defect. Since she cannot guarantee the boy will call her, the prisoner’s dilemma predicts she should not give him her number, and that her actions are, in fact “crazy.” What accounts for not only Carly’s actions, but also the success of her strategy? To answer this question, we must look beyond the constraints of the prisoners dilemma. Other models may in fact lend more explanatory leverage on the issue.

I. A Shadow of the Future

One of the most important rules at play in a classic prisoner’s dilemma is that it is a one-shot game. However, if the game is played over and over with the same actor, this is known as an “iterated prisoner’s dilemma.” In this case, since the game is repeated, each actor will have to live with the consequences of his actions after the first round is over. This added condition is called the “shadow of the future.” When a shadow of the future is present perpetually (i.e. the game does not have a set end point), the optimal strategy ceases to be one of defection and instead becomes a “tit-for-tat” strategy, in which the actors try to mirror each other’s actions (see Axelrod’s “The Evolution of Strategies in the Iterated Prisoner’s Dilemma“)

Carly opens the game by giving the boy her number, which is cooperation. Since if they were to date the game would repeat without a definite end-point, Carly calculates that it is in the boy’s rational interest to call her. Until the point that either Carly or the boy defect from the game, cooperation is the optimal strategy according to the model.

However, the reality is not quite so simple. Rationally, Carly should signal every intent to cooperate to the boy in order to maintain her credibility. Yet she deliberately tells him “Hey, I just met you / and this is crazy.” What explains this puzzling signal?

II. Signaling Intentions In The Stag Hunt

Carly’s predicament could also be explained via a model known as the stag hunt. Originally developed by Jean-Jacques Rousseau, the stag hunt involves two players who get a small payoff from hunting two rabbits separately but a large payoff from hunting one large stag together. Hunting stag requires a different weapon than hunting rabbit, however, and the weapon choice of the other player is unknown.

In a sense, Carly and the boy in question are in a sort of stag hunt. We assume for the purposes of the game that both Carly and the boy would prefer to go on a date over not going on a date (“Before you came into my life / I missed you so bad”). However, they also do not want their time wasted by trying to score a date with someone who is uninterested in going out with them. We can model the payoff structure of the game as follows: 

As the matrix reveals, there are two equilibria in the game, but one has a higher payoff than the other. When such a payoff structure exists, actors will try to communicate their intention to cooperate (ie, go on a date) in order to try to induce cooperation from the other party. Communication is a highly theorized area of international relations, which involves signaling capability, resolve, and credibility. How can we understand Carly’s communication in this regard?

Carly’s statement “Hey, I just met you / and this is crazy” is an attempt to communicate both intentions and resolve. In particular, both statements are intended to highlight the costly signals Carly is giving of her intentions. Were Carly not interested in the boy, giving him her number after having just met him, an admittedly “crazy” action, would incur significant costs. By doing so regardless, Carly is communicating that she is in fact interested in having him call her. Her willingness to challenge social norms is an attempt to communicate resolve, especially given communication difficulties implicit in the situation at hand (“It’s hard to look right / at you baby”). That is, she is in fact interested in the boy and does in fact want the boy to call. Carly supports this signaling regime by noting that “all the other boys / try and chase me” a statement that she is committed to exclusive cooperation with the boy at hand.

The addition of the word “maybe” at the end of her signal is a tactic designed to highlight the choice which the boy now has to make between calling and not calling. Schelling would categorize “maybe” as as a “trip-wire,” in which one actor sets up an automated series of events which the other actor will trigger with a certain action. Since the first actor, Carly, has already chosen a risky course of action and the decision is out of her hands, it falls to the boy to pursue a strategy with the lowest risk for himself. This also turns out to be the one with the biggest payoff for Carly as well. As it happens, the boy does eventually call, and both Carly and the boy achieve their Pareto-efficient equilibrium.

In conclusion, Carly’s strategy is actually a rational one given the payoff structure she faces in the given situation. While such an explanation cannot explain her decision in the music video to wash a car in 5-inch heels, it can explain her actions as the outcome of a rational strategy. Further research should examine the generalizability of the argument by accounting for critical cases such as “Payphone (explicit)” by Maroon 5 (ft. Wiz Khalifa) and “Wide Awake” by Katy Perry. Ultimately, such inquiry serves to provide scholars with a deeper understanding of the complex world of interpersonal relations as relayed through pop songs.

UPDATE: Duck contributor PM provides an an alternate model of Carly Rae Jepsen’s song.