Equilibrium Driving on Cornish Lanes

This is about driving on Cornish lanes (small roads in Cornwall, UK). I offer two things in this post: informed casual observations (in place of rigorous data collection) about how people navigate these lanes and a bit of game theory to explain my casual observations.

There are some things you need to know about Cornish lanes before we proceed. Cornish lanes have probably not changed since early medieval times, except that they are now tarmacked. Cornish lanes can be driven in both directions but they are too narrow for two cars to pass each other. Cornish lanes are bounded by tall and overgrown stone “hedges” on both sides. Cornish lanes are windy (not as in windswept), they meander. Cornish lanes have one final redeeming virtue (apart from being very pretty): there are occasional widenings, places in which two cars can pass each other. To be fair, there is always some widening within about a hundred yards (a yard is a bit less than a meter – we are in the UK, not in Europe) from any point along the lane.

Now to my observations. When the lane is narrow, as they mostly are, driving on the left is observationally indistinguishable from driving on the right. Yet, I think it is safe to say that whenever a road is wide enough to allow the distinction, people adhere to the general equilibrium behavior and tend to drive on the left side of the lane. More importantly whenever two cars meet they will in almost all cases try to pass each other hugging their respective left side of the lane.

Invariably, however, when two cars meet, they do so in a part of the lane that is too narrow for them to pass each other. This is due to the limited forward visibility that overgrown stone hedges allow on the meandering Cornish lanes. Now the game is afoot. We have two players, the drivers of the two cars facing each other in a place where they cannot get past each other. Ignoring the fact that time could play a factor in this game (after all, in any model, we have to sacrifice something of the full complexity of the real life problem in order to provide some basic key insights into the problem) the two players have essentially only two strategies: they can simply not move or alternatively they can back up to the nearest widening of the lane (which as I said before, is never too far away). I now turn to the payoffs in the game. I think it is safe to assume that essentially every driver would prefer not to move over backing up. It is probably also safe to assume that every driver would prefer to back up if the opponent does not (to enable her to eventually get to her destination). I agree that, as I will ignore time as a factor in this game, I am ignoring potentially interesting and amusing waiting games (or so called games of attrition). While these could theoretically happen, I have actually not encountered any in my, admittedly limited, experiences here. This further justifies my omitting time from the model I describe here. According to the model I thus described here the two drivers are facing a game of anti-coordination as the game theory literature would have it called. This game has three equilibria. One in which both players randomize with a high likelihood of getting stuck forever. This is empirically implausible, so don’t worry if you do not understand what I mean. The other two are such that one driver waits while the other backs up. This is invariably what happens. However, the interesting thing I want to address here is how it is determined who of the two drivers should do the backing up.

In what follows I describe my observations regarding the behavior of locals when they face such a situation (and they do so many times every time they drive). First, a local will try and establish what type of “opponent” (if I may call them that) she or he faces. By looking at and analyzing a variety of “signals” a local would first try to identify whether her opponent is a local or not, also taking into account the season. In the summer there are many more tourists than at other times of the year. Perhaps the most important among the signals (or signal generating processes, one should probably say, if one wanted to be a careful game theorist) the locals look at are the license plate and the general state of the opponent’s car. A foreign license plate is a fairly precise signal that the opponent is not local. There also seems to be something in the British license plate lettering and numbering system that, although a mystery to me, allows locals to identify (with lower precision) a Londoner or Northerner or generally somebody not from the area. If the opponent car is expensive and shiny, then it is also unlikely that its driver is local. Most local cars have scratches along their left side as the frequently hug the hedges almost a tad too closely. In fact locals often remark on the tourists’ apparent reluctance to drive their cars close to the hedges.  Other signals include the speed of the oncoming car, both too fast and too slow are indications of non-locals, and how far the opponent car is from the hedge on their left side (see above).

If a local attaches a high likelihood that their opponent is non-local (and all this is done before the cars have even come to a standstill) then they immediately put the car in reverse and back up to however far back they have to go. This is due to their belief (tested just sufficiently often) that non-locals are simply not good at backing up and take ages doing so.

If a local, however, attaches a high likelihood that their opponent is also local, then the game, which to the game theorist is a game that is ex-ante a game of incomplete information, now essentially becomes a game of complete information. If you are not a game theorist, ignore this last sentence. What I mean is this, we are now in a situation where both drivers are pretty certain that they are facing a local. Locals, as they both know, know exactly where all the widenings of the lane are. Almost invariably now, I find, that it is the person who has the easier backing up to do (e.g. the person who has less far to go back to the next widening) who does the backing up.

Locals, thus, manage to solve this complicated anti-coordination game in the most efficient way. They are all happy to follow this societal norm of behavior for two reasons. First, it is an equilibrium and if any driver decided to do something different it would only cause her or him more delays. Second, this norm is such that on the whole every driver would have to back up in approximately half of all such situations. This is because any given driver would find herself in the “better” position of being further away from the next widening in the lane than her opponent in approximately half of all such situations.

What two non-locals do I do not know.

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