Prisoner’s Dilemma Denim Style

At work denim was removed from the acceptable dress code. No worry to me because I could not remember the last time I actually wore jeans to the office. They are not clothes I wear often away from the office either. Even in “cold” weather (above freezing, below room temperature) I sweat in them. I find them uncomfortable to wear while sitting. So I pretty much only wear them when I am going to spend time in freezing weather and not at the office. Losing the authorization did not bother me much.

Your area has been assigned a denim dollar collector for “Denim Days” starting ******.   Each [certain weekday] your denim dollar collector will visit to see if you or everyone in  your area is wearing denim.   If everyone in your area is wearing denim the cost will be $3.00 per person, if not, the cost will be $5.00 per person.

I wonder if people know this is a more complex version the Prisoner’s Dilemma in game theory.

Tucker began with a little story, like this: two burglars, Bob and Al, are captured near the scene of a burglary and are given the “third degree” separately by the police. Each has to choose whether or not to confess and implicate the other. If neither man confesses, then both will serve one year on a charge of carrying a concealed weapon. If each confesses and implicates the other, both will go to prison for 10 years. However, if one burglar confesses and implicates the other, and the other burglar does not confess, the one who has collaborated with the police will go free, while the other burglar will go to prison for 20 years on the maximum charge.

The strategies in this case are: confess or don’t confess. The payoffs (penalties, actually) are the sentences served. We can express all this compactly in a “payoff table” of a kind that has become pretty standard in game theory.

In this case, cooperation is both confessing (example) and wearing denim (situation). Defection is both not confessing (example) and not wearing denim (situation). Unlike Prisoner’s Dilemma there is not a middle point where both defecting has the second best result. Also, one has to anticipate whether 3-30 people all cooperate not one other. According to game theory, it is in everyone’s interests to cooperate which means wear the denim.

Unfortunately, there is a plausible third choice which may derail the whole thing: refusing to pay anything. Wearing jeans and not paying would still be unauthorized as the point of the activity is to raise money by letting people participate. However, forcing people who do not wish to participate seems like a Human Resources disaster waiting to happen. Yet, the game is predicated on universal participation. Hopefully, when there is push back from people like me they just strike those refusing to play along from the activity as non-participating and do not punish all the members of the group by making them pay for a non-participant.

BTW, Denim supposedly could mean “de Nîmes” aka “of Nîmes” a city in France. (Wikipedia / Yahoo news) I didn’t go into scholarly research to determine whether that is true.