The Breakup Game

My mom always used to say to me, "Honey, the only way to get over someone is to get under someone.” –Marsha Mason as Sherry Dempsey on Frasier, 1997.

The dissolution of a romantic or any other significant interpersonal relationship is stressful, typically for both parties, the person executing the breakup (here: the dumper) and the person receiving it (hereafter: the dumpee). The aftermath is rife with emotions, and mostly negative ones. Thankfully, emotions fade with time and finding a new relationship can hasten the recovery.

In economic and behavioral terms, a breakup is clean if all transactions cease. Achieving this outcome is sometimes not possible, as when parents need to continue to coordinate their efforts in order to care for their children. Let us therefore consider the simpler case of a youthful romantic break-up, and specifically the case in which one party refuses to consent to the withdrawal of the other. In such a case, we find interpersonal dynamics that are more driven by strategy than by love.

The unwilling dumpee may resort to coercive tactics to win back the dumper. The wisdom of such coercion is questionable because even if successful, the dumpee cannot be sure that the dumper has returned to an attitude of love when it is at least as likely that they merely acquiesced under duress.

Both parties’ behavioral choices reduce to two broad strategies, one accommodating (i.e., cooperation c) and another confrontational (i.e., defection d). As such, the space of possible outcomes can be displayed in a two-by-two matrix, where higher numbers refer to a party’s more preferred results. In the figure, the dumpee is cast as the row player and the dumper is cast as the column player. In each cell of the matrix, the former’s (latter’s) preference is noted by the number to the left (right) of the comma.

The break-up game preference matrix

Source: J. Krueger

We can now imagine the dumper moving first with the dumping, that is, an act of defection. The dumpee then finds themselves confined to the right half of the matrix. Their best response is to accept the bad news by cooperating. The upper-right cell of the matrix depicts this outcome, which is a Nash equilibrium. Neither party can improve things for themselves by switching strategy. Arguably, this is how most of the break-ups in the (formerly) romantic world go down.

A dumpee, however, who has read—and perhaps misunderstood—Brams, Ellsberg, or Schelling may try their hand at a mad-dog move and reject the break-up. A bold, and fortunately rare, gambit is for the dumpee to threaten self-harm in hopes that this will prompt the dumper to reconsider. In the matrix, this move is represented as a step down from the upper right cell (2,4) to the lower right cell (1,2). A dumpee attempting this might think that the dumper will then cooperate, moving the outcomes to the lower left cell (4,1). That the dumper would accept the cost of going from preference = 2 to preference = 1, could be predicted only if it were also thought that the dumper would also expect the dumpee to then cooperate, which would result in the equable and efficient outcome shown in the upper left cell (3,3).

In other words, if the dumpee were thinking as clearly and strategically as assumed in this model, they would need to have grounds for a higher-order theory of mind; they would need to feel justified in thinking that the dumper is not only, in part, motivated by altruism, but also that the dumper has expectations about the dumpee’s eventual response, that is, cooperation. After the dumpee’s initial act of defection, this is obviously a tall prediction.

This modeling exercise may seem idle because of the unlikelihood of finding sophisticated prospective reasoning in someone whose social world has just entered a stage of mortal danger. Even if the dumpee’s calculations were accurate and initially fruitful, one would have to wonder how stable and happy a thus-restored relationship might be.

We could console ourselves with the thought that mad-dog strategic moves belong to the worlds of politics, finance, and shady business dealings. Romance is supposed to be pristine, even in its stages of dissolution. Then again, the prospect of losing an object of social and sexual desire can bring out choices, schemes, and signals that mimic what a cold-blooded calculator might do. Game theory makes no room for the autonomous nervous system, but it can model the havoc this system may wreak on human happiness.