Grand Central Station and Adam Mickiewicz
Thomas Schelling, in an analysis of coordination, described a situation in which two people wish to meet in New York City on a given day, but cannot communicate the time or place at which they should meet. At the time, he suggested that beneath the clock at Grand Central Station at noon would be an ideal time and place– a “focal point” for coordination. He no longer believes this to be the case, as he explained in an interview with the Richmond Fed. When he originally formulated the question, rail was one of the most common ways to arrive in New York, making the clock at Grand Central Station an obvious choice. Now, with the decline of rail travel, it’s not so obvious where one should expect to meet another. Tyler Cowen asked where the new focal point might be, and has received a variety of responses. There appear to be two general categories, however– presumed focal points based on common knowledge, and those based on a personal connection.
For example, if two individuals who did not know one another were to meet in Chicago, a likely choice would be in front of the Hancock building– simple enough. But what of the case Lewis Black describes in “Nothing’s Sacred”, in which he enters a dorm at a school he’s visiting, leaving his dog Jack-Jack outside? When he returns, Jack-Jack is gone. He searches, but cannot find his dog. It was his dog, so naturally he did not communicate a time nor a place at which to meet should they become separated. Lewis panicked and searched everywhere, but could not find his dog. The next day, however, Jack-Jack returned to the spot at which Lewis had left him, at the exact time he had left him. Both knew, through common experience, that it was the ideal time and place at which to meet.
Coordination games such as this apply to more than just meeting other people. Please remember, though, if you’re ever lost in the woods, stop running around like an idiot. People really do die that way. Many different situations are similarly dependent not on the actual choices that the individuals make, but that they choose the same (or compatible) actions. Many of these are enforced by law– driving on the right side of the road (or left, in a few places), flying at certain altitudes based on direction of travel, et cetera. Many more are enforced by social convention; do you extend your left hand or right (or neither) when greeting someone in country X? Interestingly, if apply this social context to the meeting place game, we may find that people perform more poorly at it today than they would have 30 years ago. Since communications (read: cell phones) have improved so greatly in this time, the need for coordination has diminished, and thus people no longer rely on a central point for coordination. In short, the practice of meeting friends has become decentralized, and as a result, people have less practice at the coordination game.
To couch it in terms of game theory: if we imagine a repeated version of the game, in which the players are still not allowed to explicitly communicate, but are allowed to know the choice made by the other player in the previous round, we can imagine that eventually, the players would choose the same meeting point. In all successive iterations of the game, they would be best off if they continued to choose the same location, and thus a focal point would emerge. In the rounds between the first round and a successful meeting, the optimal strategy might be to choose randomly (50/50 chance) between remaining at their previous choice and choosing to meet at the other player’s previous choice. In each of these rounds, there would be a 50% that they would meet. This pattern, in which the players’ initially poor outcomes give way to a stable equilibrium, likely cooresponds to the learning process my generation would have to endure if our cell phone service were to die.
Interestingly, Poland seems to have this one down. In every city (or, at least, so it seems) there is a statue of Adam Mickiewicz, which serves as a de facto meeting place. Could this be due to the relatively slow development of their telephone infrastructure? I’m acutely aware that calling Poland can be ridiculously expensive, and according to The Economist, mobile phone subscriptions only six years ago were as low as 10.6 per 100 people. Until recently, then, social conventions had to help people find one another. Cell phone use has exploded in the intervening years– will Adam Mickiewicz be lonely?