The logic of inappropriateness

Below, Scott Weiner argues that Carly Rae Jepsen’s song “Call Me Maybe” is an illustration of the dynamics of standard game-theory models, specifically the prisoner’s dilemma and stag hunt. Weiner assumes that Jepsen is a rational actor, that both Jepsen and her beau are better off being together than being apart or with different partners, and that Jepsen is rationally choosing to communicate her availability to facilitate their coming together. I share these assumptions, but as I demonstrate Weiner misses the key points of the song. If, as Weiner suggests, both Carly and the boy are better off together than apart, then why signal that “this is crazy”? And why is the song called “Call Me Maybe” instead of “Call Me Right Now So We Can Be Together”?

The answer is that Carly is trying to communicate that, despite her forward approach to the boy, she is nevertheless suitable for him. Sometimes, disclosing more information hurts rational actors, and for Carly to disclose that she is interested in the boy after having just met him could signal to the boy that she is an undesirable partner—not just because of old-fashioned notions (“she’s not wife material“) but also because an aggressive partner of either sex might not be interested in a long-term relationship (Hall and Oates, 1982).

So we are left with a puzzle. If Jepsen is rational and can assume her potential partner is as well, why pursue a strategy that both stresses her availability (“call me!”) while highlighting her ambiguity (“maybe?”) and stressing that the situation is causing her to behave in an unusual way (“and this is crazy”)? The answer lies in the fact that dating is a game played under asymmetric information, which changes the dynamics of the interaction in ways Weiner does not appreciate. I provide an informal treatment below.

Assume there’s some distribution of types of potential dating partners in the world, “worthy” and “tragic.” (We assume that the dating game is multiple-shot; as is well understood, one-shot romantic games have dramatically different properties.) The preference of each player, worthy or tragic, is to find a worthy partner and to avoid ending up with a tragic partner. Worthy partners would rather be alone than with a tragic partner; tragic partners would rather be with a tragic partner than alone.However, although every player knows his or her type (that is, whether they are themselves tragic or worthy), they can’t know with certainty whether other players are. Consequently, players who advertise themselves as worthy may be lying, and there’s no way to tell in advance.

How, then, for worthy partners to advertise themselves as being worthy? As Schelling and others would point out, there has to be some sort of credible signal. This, however, is likely to be reticence, since tragic partners are made much better off by being with anyone than by being with the right partner. Consequently, the dating scene is likely to be made up of tragic partners pretending to be worthy ending up with each other. (Game theory is often realistic that way.) This is a perverse equilibrium: The only players left on the scene are the ones who shouldn’t be dating anyone, because all the worthy partners know that trying too hard puts off other worthy partners.

Let’s assume, however, that Carly and her boy are both worthy. If Carly comes off too strong, then the boy may assume that she is tragic. So she instead engages in signaling by saying that she’s not normally this way, that the situation is highly unusual, and that she’s putting off all the other boys who are interested in her to talk to the boy–all signals that she is interested but not tragic.

Unfortunately for Carly, the ploy is unlikely to work if the boy is a worthy partner. While Weiner does not provide an independent assessment of how likely Carly and her object of attraction are to end up together, his analysis suggest that they will be happy together because they are better off together. Alas, my analysis suggests instead that all such posturing will be dismissed as merely cheap talk.