I live in a suburb of Tel Aviv. Every morning during rush hour the two streets leading to the highways to Tel Aviv are packed. I try to evade going to the university during rush hour. Unfortunately, the kids start school at 8:30, and therefore quite often I have to trail to Tel Aviv with many other sleepy parents.

In some countries driversĀ keep their lane while driving in a multi-lane packed street. This is not the case in Israel. People believe that by changing lanes they can get to their destination faster, even when all lanes in the roadway are equally packed. Plainly one can rationalize this behavior, as one lane may be momentarily faster than the other, and therefore by changing lanes one can progress a little faster.

The streets leading from my home town to the highways consist of four lanes, two lanes leading from the town center to the highway, and two lanes leading from the highway to the town center.

The other day I was going to the University, and the two lanes leading to the highway were packed as usual. I noticed that the car in front of me tries to change lanes. Then I noticed that the car in the other lane also tries to change lanes. Thus, each driver believed that the other lane is faster than his own lane. As they were driving one next to the other, their intentions were common knowledge among them. But then, as Aumann tells us, it should be common knowledge among the two drivers that both lanes are equally slow. Nonetheless the two drivers switched lanes.

Anyone has a good explanation?

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## 10 comments

March 26, 2012 at 7:14 am

RonIt is probably the illusion of control.

March 26, 2012 at 1:00 pm

OriMaybe they didn’t study game theory?

March 26, 2012 at 4:01 pm

SandipI suppose, optimal strategies become habits, habits become conventions, and ppl keep following the strategy even if it is no longer optimal!!

March 27, 2012 at 2:41 pm

El GauchoIt’s common knowledge that they want to switch lanes not necessarily that the lanes are equally slow. Each person might feel he is better at judging the right time to switch than the other.

March 28, 2012 at 3:33 am

Paul GoldbergA well-timed lane change is very satisfying. And there is the hope that it becomes the first of a sequence of fortuitous lane changes, in which the motorist has managed to catch the rhythm of the highway and is truly “in the zone”.

April 1, 2012 at 11:57 am

Hannu SIf Alice tries to switch lane and overtake Bob, Bob’s best reply might be to switch lane as well. Because the line behind Alice after her move becomes congested and slower: Bob probably has to brake if he doesn’ switch.

April 6, 2012 at 2:07 am

Peter TThere’s a public transport rule of thumb that goes that people value wating at three times movement, and unanticipated witing at around 10 times. In other words they will drive for 30 minutes rather than wait 10 and ride 10. Same thing here – going to work is supposed to be “moving”. Changing lanes is “moving”, and it’s better than waiting. Even if it does not actually improve your arrival time.

April 6, 2012 at 12:42 pm

JeffYou might find this article of interest: http://people.brandeis.edu/~moshep/Projects/DoTheyReallyMoveFaster/133.redelmeier.pdf

April 6, 2012 at 1:21 pm

lackThe problem of changing lanes is a good problem that is corrently studied by many engineers. There are three opinions, one that is good and the other that is not convient and the remainging it is the same. The leading person that believes that is the same or equal is the leader engineer Daganzo, and many other engineers specially at the Institute of Transpotation at Berkeley, that are concerned with this difficoult problem. Personally I do not know the answer because here in Mendoza, Argentina there are not highways of four lanes. I will think about it. However I would like to point out that perhaps the answer may be studied by obtaning an inmediate solution from my paper On Urban Traffic, Mathematical Models in Economics, Eds, J.Los and M.W. Los, North Holland Publishing. Pag 461-475,(1874). Here in this paper, we study solutions of extensive games much more general of those actually studied.We apply them in dynamics for traffic problems.We prove the existence of Nash equilibrium and the Em-stable points in them and dynamically. Some of these concepts where introduced by me in Em-Stable Points in : Simple Stability of General n-person Games: Naval Research Logistic Guartely, Vol. 14, No 2, Pag. 163-171.June 1967 and connected with E-Points after that.

In the first we are concerned with the problem of lanes perhaps not the exact one formulated by Aumann.I think that a small modification of my paper will arrive to the real conclusion of it. Another personal contribution of related topics in transportation networks is Competitive Aspects in the Scheduling of a Simple Transportation Line Mod., Sim. and Con, C, AMSE Press, Vol.22, No2, 1990, pp.41-64,Here we obtain an optimun or Nash solution when there are stations, or intermidiate stoping points in the transportation network. Unfortunately, the game theoriests are not aweared of these contributions and in the modern literature they do not appear.

Personal I think that using my material together with the entire transportation and traffic theory developed by many scientiests with the engineers opinions and perhaps some fundamental help needed by other people working in game theory who now lack important theoretical models,specially for transportations and traffic, one can arrive to excelent answers. I quote the paper of J-D Smmocker,M.H.Bell,F, Kurauki, and H. Shomamoto:A Game Theoretical Approach to the Determination of Hypergraphs in Transportation Networks, Transportation and Traffic Theory 2009: Golden Jubilee. Eds.H.K.Lam,S.C. Wong and H.K. Lo, Spinger, pag 1-18.2009.that is a good modern study about the problem of obtaining a good solution of getting the best path in a city. With good modifications is clear that is a good tool for the problem presented by Aumann.This is the most important one concerned in the traffic theory since the years 30s, when the pioneers of this matter, as Waldrop, Hermann and Prigogine (1974),Charnes and Cooper (1962-3), etc began to apply important ideas in the study of traffic in a highiway and in a city. Charnes and Cooper where the first to introduce equilibrium points for the solution of the best path. This was done about the years 60 and euristically. After this the same authors in their famous book regarding linear probramming, game theory, etc specially for operation research they began to study the global problem of opimization in traffic flow.Hermann and Prigogine wrote their fudamental book in 1974 explainig theorically for the flow in a highway with some good explanation about the curve regardingthe flow, the density and velocy in a simple highway.They finish the last chapter telling that in a city one has to apply game theory. From that date there are many jounals, books, etc studing all problems. We mentions some of the them as Patrickson, Cascetta, Daganzo, Hartmann etc.The german scientiests Schrenberg, Wolf,Bachen (1995-1997) have studied many problems of traffic flow and granular flow The literature is full of models with the continuty equation and partial differential equations of the hidrodynamics There are actual workshops in this area and also articles and related topics with the equation of Boltzamnn, see for example the News Review (2011). They genelly provide computational programs, which generally work well in some simple cases in the practice. Generally for cities they lack to fullfil the reality and fail. Let me tell you that I have done some works in the problem of green wave in cities of different structure of topology in 1995-1997. I introduced the LAUMAR systems which are structures not yet studied in a vectorial form that permit to have a dynamics series of vectors passing together in a perpendicular way in a rectangular grid , solving the called Manhattan problem. We also with Tarazaga have applied these to lazer with good results. Finally in the last years you find in Prepints of IMA University of MInnesota (2010-2011) I

published two papers of mine solving the problem of coordination of green light in double way avenue and in a rectangular city with all double avenues obtaining a sufficient condition for having it. I have much interest to follow the study the one of the most difficoult problems that is the coodination of lights traffic in cities.I invite anybody with interest in this area to cooperate with me in any kind of future study.

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April 6, 2012 at 1:24 pm

ezio marchiSorry I commited an error.

Lack is Ezio Marchi