It’s midnight and a loud bellow screeches across the jersey shore. “It’s t-shirt time” yells Pauly D, a signal for the guys to put on their freshest t-shirts before the “cabs are here”. At the club, Mike, Vinny, and Pauly (MVP) operate under a dual mandate not much different from the Federal Reserve. But MVP isn’t on a mission to foster an economy that maintains stable prices and sustainable employment. Instead, they create an environment conducive to fist pumping and picking up girls with policy tools of staying fresh to death. As many episodes have unfolded, the journey from Karma to the shore house isn’t always simple. Sometimes poor decision making on the part of the cast impedes their progress to the ultimate goal. This is no different than how many investors approach the market, and with a little game theory, both the lovable first pumpers and many investors can make better decisions.
What is the Secretary Problem
Using the secretary problem in decision theory offer an interesting solution to this callous problem. Suppose Pauly D meets 20 women on a random Friday at Karma. Each candidate is met one after the other and for the sake of this example, without the help of his most trusted wingman, Vinny. After exchanging pleasantries Pauly must make a decision. He can commit to the women for the rest of the night or move on to the next one, not knowing if future candidates will be any better. Rejecting someone immediately removes them from the selection pool and they can no longer be contacted in future interactions.
Pauly now has a few options. Common knowledge suggests turning away the first person because there is plenty of fish in the sea, but waiting until the end of the night might lead to a suboptimal decision. The question is to find a stopping point that maximizes the probability of selecting the best suitor.
The secretary problem prescribes rejecting the first ~n/e candidates—where n is the number of applicants and e the base of the natural algorithm—and selecting the first applicant that exceeds the initial training set. Using this method offers a better than one in three chance of making an optimal choice. For Pauly, that means turning away the first seven of the hypothetical 20 suitors before considering a decision about the night. In the show, though, it appears as if the group makes a choice early in the night with the exception of any “grenades”.
An extension of the secretary problem provides a better solution by skipping the first (n^1/2) – 1 applicants before making a decision.
How Game Theory Improves Decision Making
Now suppose Mike and Vinny arrive at Karma late. It would be difficult for Pauly to make an optimal decision using the secretary problem alone. He is going to face new competition and someone in the group is bound to cause a problem. In season 2, for instance, The Situation attempts to pull the robbery on Vinny’s girl Ramona and in a later season he pulls the same stunt with Pauly’s ex-girlfriend. The clear breakdown in group dynamics—fighting, shouting matches and attempted robberies—and coordination failure often leads to unpredictable outcomes.
Applying a basic game theory strategy answers this problem. The first option is to ignore the other guys and wait for the ideal candidate, a classic wait and see approach. This means Pauly’s reacts to the actions of his friends, and in effect, seizes the second mover advantage when it exists. Pauly can also help Mike and Vinny find a girl to distract them from the other women in the bar, otherwise known as the wingman theory. This clears Pauly to go back to running the strategy outlined by the secretary problem.
As we’ve seen, it’s all about timing. The goal is to take actions that will maximize rewards and minimize costs, a theory that influences many life choices including stock trading. In the context of financial markets, the secretary problem comes down to determining an optimal stopping strategy. That is closing a position at a near-term high when future prices are unknown. The objective is to maximize the chance of selling at a high given a random sequence of fixed length. Here, traders also hold the stock for a given amount of time and use the remaining time to sell at some given event.
The secretary problem supports some conventional wisdom about dating, consumer behavior, and financial trading. But the truth is many life choices come down to individual preferences that can’t be modeled by equations.