Living in the the dorms, I stumbled over ping pong balls and red solo cups more than once going into the only kitchen on our floor.
I never participated in drinking games like beer pong, but I’m familiar enough with the drinking culture on campus to know that Thursday—Thirsty Thursday—is the night to go out drinking.
Szilagyi considers a similar culture in his paper on the El Farol Bar Game, a game theory problem about a popular bar in Sante Fe. He proposes a solution to the problem far simpler than approaches come up with by others in the past.
By considering players of a particular personality type, he finds their decisions become increasingly accurate and stable as more start to play.
The Drinking Culture. In the El Farol Bar Game, every Thursday after work, all the employees of a company across the street want to go out and have a drink. However, the bar can only hold 60% of them!
The rules of the game require that the players—the employees, say, of Big Web Company—decide whether to go to the bar at the same time and without talking with one another.
This rule means that if everyone thinks the bar will be empty, then it will end up over-crowded. Conversely, if everyone thinks the bar will be crowded, then no one will go at all.
Far Simpler. Szilagyi, for another paper, developed a software package for game theory simulations. This software is general, so with minimal reconfiguration he adapted it for this drinking game.
He imagines—and his software creates—an array of players, each with his or her own personality. Built into the software are the personality types:
- Conformists, or players who do whatever the majority did last week
- Greedies, or players who mimic the actions of whoever’s made the best decisions so far
- Predictables, or players who have a chance P that determines whether they go to the bar on any given day
- Accountants, or players who base their P on an average of past good/bad decisions
- and Pavlovians, or players with a P they increase/decrease as they figure out the proper ratio of going/staying home
Accurate and Stable. After introducing these five personality types, the author decides to focus only on the last, Pavlovian. I found this transition abrupt, although not as abrupt as his four line conclusion.
I needed to spend an hour working out where Szilagyi was getting his numbers, but I finally understood why he chose this personality type. The strategies of Pavlovian players in choosing between going to the bar and staying home have a special relationship.
Turning this relationship inside-out, so to say, Szilagyi determines the best “payoff function” for his solution to the game.
Simply put, payoff functions are from game theory and decide how a player feels after making a good or bad decision—happy about staying home when the bar ended up overcrowded, for example.
When his function is worked back into the Pavlovian relationship, it results in precisely the right percent of employees getting drunk each night, all without them breaking the rules of the El Farol Bar Game. ∎