Using a Payoff Matrix to Figure Out If You Should Get a Divorce
Nearly half of all U.S. marriages end in a divorce (according to the American Psychological Association). There are many reasons that can spur this unfavorable outcome, but infidelity is arguably the most stigmatized one on the list. The psychological harm that cheating can inflict on one’s partner is something that I wish upon nobody. However, these cases of adultery make for an interesting Game Theory problem.
For example, consider a simplified overview of the story in the article above. Lucy from Delaware must decide whether to divorce her cheating husband. The divorce is not so simple because the husband (who will we refer to as Trey for “betrayal”) has recently inherited 75% of his father’s estate, which is worth $3 million. To further complicate the considerations for Lucy, she has had 5 children with Trey. Moreover, since Lucy and Trey live in Delaware, divorce courts follow “equitable distribution,” meaning that the judge gets to deem what is fair and appropriate. This implies she may not get as much of his estate as she would effectively get by staying with him.
Though the following will be a gross oversimplification of the article above, we can try to focus on the two most important strategies of Lucy and Trey to figure out what equilibrium will arise in this so-called divorce game. For Lucy, we will say she can choose to either DIVORCE or NOT DIVORCE Trey. Trey, on the other hand, can decide to either ADMIT or NOT ADMIT to his infidelity. Given this model, we now construct a payoff matrix. Note: there are many unknown values we can not quite fill in values for, so we will leave these as parameters to the model that are decided by Lucy and Trey.
There are some things that are important to note about this model. First, we assume Trey, being the one who is cheating, is indifferent to every other cost besides protecting his estate. Secondly, we only represent losses to his estate, since it already is in his possession in the eyes of the model. Lastly, we arbitrarily decide that it would be likely for Lucy to get 50/50 of Trey’s estate in court when Trey denies cheating (which makes him look like a liar), whereas she only gets a third of the estate when he admits to his wrongdoings. It might also seem weird that Lucy gets the entire estate when she decides to stay with Trey and he loses none of it, but again this model simplifies a very complex situation. We have no way of knowing how the two of them share wealth in marriage.
Without knowing parameters, it is unclear how this game will play out, especially since Trey has no dominant strategy. However, if we were to find out the result of their game (i.e. which strategy each chooses), we could reverse engineer the problem and figure out which parameters were more important to Lucy, be it keeping family, escaping Trey, or getting closure with Trey. Additionally, if we could repeat this ideal game repeatedly with multiple identical couples, we could observe the frequency with which certain Nash equilibria occur and determine our parameters using the assumption that payoffs must be probabilistically equal.
In the end, it is up to Lucy to decide what she really values in her life. There are too many complexities to ever know exactly what payoff Lucy received from the divorce (or to put it better, the costs she incurred). However, our model has given us a better framework for important life decisions, and maybe important insight for our friends who need marriage counseling.