Game Theory and Tardiness

Imagine the following situation: two good friends decide to have dinner at a certain restaurant and agree to meet each other at the restaurant at five-thirty in the evening.  Whether or not they honor their established meet-up time can be seen as a game theory dilemma.

In the situation there are four alternatives: (1) they could both show up on time; (2) friend A could show up on time and friend B could show up late; (3) friend B could show up on time and friend A could show up late; (4) they could both show up late.

Now, because time is infinite, alternatives 2, 3, and 4 are vague--they fail to specify the exact moment in which one or both of the friends arrive (example: in alternative 4, both friends could show up late but at the same time, or they could both show up late but with one friend showing up before the other).  So, to clarify things a little bit, lets just state the four alternatives as:

(1) they could both show up on time, at 5:30pm
(2) friend A could show up earlier than friend B
(3) friend B could show up earlier than friend A
(4) they could both show up late but at the same time

Alternatives 1 and 4 are optimal.  In alternatives 2 and 3, one person has to sit around waiting for the other to arrive.

What is interesting is that in punctual societies, like the United States (or stereotypically Germany and Japan), there exists a socially ingrained consensus to choose alternative 1.  In countries where such a socially ingrained consensus does not exist (stereotypically non-punctual societies: the developing world), each individual shoots for alternative 4, but ends up with alternatives 2 or 3.

In a punctual society, friend A believes friend B will show up on time, and friend B believes the same thing with regards to friend A.  They, therefore, both show up at 5:30pm.  In a non-punctual society, friend A believes friend B will show up late, and friend B believes the same with regards to friend A.  Friend A will, therefore, show up late, in order to avoid showing up on time and waiting around for his friend who he assumes will be late (he wishes to avoid alternative 2).  Friend B will do the same (in order to avoid alternative 3).  The problem here isn't that they both decide to show up late, since it's possible that they could both show up late but at the same time (alternative 4).  The problem is that they never establish when they will arrive, leaving it up to each individual to try to guess how late the other will be.

For this reason, alternative 4 becomes the optimal choice, but only after alternative 1 has been discarded.  Once one person starts showing up late, the other tries to match the exact tardiness of the first.  Unfortunately it leads to a situation where the primary concern of the individual is to avoid ending up as the "chump"--the person left waiting around.  This can have unwanted consequences.

For example, lets say that friend A shows up 15 minutes late to the restaurant but finds that friend B has yet to arrive.  Friend B ends up showing up 30 minutes late.  In this case, the next time the two friends make plans to meet up friend A might decide to show up 45 minutes late to ensure he doesn't end up as the "chump" again.  Lets imagine that in that second meeting friend B shows up 30 minutes late again, but after realizing that friend A showed up 45 minutes late, he decides that next time he'll show up an hour late.  A vicious cycle ensues, with each friend trying to one-up the other and with both friends being forever stuck in the worst-case scenario: alternatives 2 and 3.  It's a difficult cycle to break, because the winner is always the tardy person.

Certain non-punctual societies are better at reaching alternative 4 without suffering the pitfalls of alternatives 2 and 3.  In these societies, people still show up late, but there is an expectation as to how late they will tend to show up.  In other words, there is a "fashionably-late norm" that establishes how long after the meet-up time a person should arrive.  In the United States the "fashionably-late norm" applies to informal large gatherings, like parties or barbeques; in many developing countries, the "fashionably-late norm" applies to both formal and informal events.  From business meetings, work presentations, and town-council gatherings to parades, parties, and dinner reservations.  The more ingrained the "fashionably-late norm" is in the society, the closer the society will be to reaching alternative 4.

A society with a well-ingrained "fashionably-late norm" should, theoretically, be just as efficient (optimal) as a punctual society.  In fact, a "fashionably-late" society is a punctual society.  If, in a society with a "fashionably-late" norm of 30 minutes, a gathering is scheduled for 3:00pm and everyone arrives exactly at 3:30pm, then everyone has been punctual according to the norms of the society.  No time has been lost waiting around, nobody has been left as the "chump."  The results are the same as if they had all arrived at 3:00pm, as we would expect in a so-called "punctual society." (We are ignoring whether these gatherings have strict "end times" or "closing times" that  cannot be altered, which would cause the "fashionably-late" society to have a shorter meeting.  This can be remedied by having the "fashionably-late" society set the meet-up time 30 minutes earlier, at 2:30pm, to have everyone show up at 3:00pm.  This may seem ridiculous [I mean, why don't they just show up at 3:00pm in the first place!] but it is a practice that occurs in "fashionably-late" societies.)  "Fashionably-late" societies are usually mistaken for non-punctual societies by outsiders who are unfamiliar with the societies' norms.  To the outsider, people seem to be showing whenever they want, when really they are showing up at the established meet-up time (the outsider is simply showing up early).

I'll finish by stating that while it may be tempting to view "fashionably-late" societies as punctual societies (as I have done above), this is only in theory.  In practice, "fashionably-late" norms are never as concrete as: "show up exactly 30 minutes late."  They tend to involve the word "around," as in: "show up around 30 minutes late."  For some people "around 30 minutes late" means 35 minutes late, for others it means 45 minutes late.  In other words, while it is true that these societies get closer to alternative 4, they never actually reach it completely.  And there is always the lingering possibility of getting trapped in a vicious cycle of alternating between alternatives 2 and 3.