## Mamihlapinatapai

The 1994 Guiness Book of World Records has a strange entry: Most succinct word. The title goes to “mamihlapinatapai”, a Yaghan word from the Tierra Del Fuego archipelego. A translator will be quick to tell you that this word is one of the most difficult to translate, but in English, its approximate meaning is “the look exchanged between two people when each is hoping the other will offer to do something that both parties desire but neither is willing to do”. While undoubtedly interesting for both its brevity and meaning, the concept of mamihlapinatapai also lies at the heart of what is known as the “Volunteer’s Dilemma”, a scenario related to the “Prisoner’s Dilemma” examined in class.

The Volunteer’s Dilemma is an N-player (i.e. 2 or more people are involved) social dilemma. It works like this: Of the N people involved, only one need “volunteer” (i.e. pay some cost) in order for everyone to enjoy some benefit. For example, you and a couple friends go bowling in Helen Newman Hall, which has a jukebox. Who will pay 99 cents so that your group can listen to its favorite song? The dilemma in situations like this one is pretty intuitive. Everyone wants to reap the benefit, so each individual is willing to volunteer if it is clear that no one else will. However, if it seems that someone else is willing to volunteer, then each individual would prefer that someone else make the sacrifice for them. While the volunteer may have to make a trifling sacrifice, there are also scenarios where potential volunteers may have to make a snap decision and risk serious injury or even death. Take for example the 1964 case of Kitty Genovese, who was in her apartment complex courtyard when an assailant raped her and stabbed her to death. 38 of Ms. Genovese’s fellow apartment complex residents saw the attack, yet the police were not called until after the woman was dead. This frightening example states another intuitive property of the Volunteer’s Dilemma: it is a symmetric Nash mixed-equilibrium problem where the probability of an individual volunteering is an exponentially decreasing function of the number of people involved. Such Nash mixed-equilibria are the same as what we have discussed in class, with the distinction that the Volunteer’s Dilemma may have any number of people and thus is potentially a much more complex problem than the Prisoner’s Dilemma. Because of its usefulness in modelling real-world scenarios and its complexity, I find the Volunteer’s Dilemma to be an extremely interesting extension of the work with Nash Equilibria we have done in class.

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