Solutions

 

                                                     You Can’t Always Get What You Want

I saw her today at the reception
A glass of wine in her hand
I knew she would meet her connection
At her feet was her footloose man
No, you can't always get what you want
You can't always get what you want
You can't always get what you want
But if you try sometime you'll find
You get what you need 

What you want is your User Optimal.  What you get is a Nash Equilibrium.

By profession and training I am a traffic engineer.  When there is merging traffic ahead, “Road narrows by one lane ahead”, what are traffic engineers trained to believe will happen? 

Traffic engineers are trained to believe that everyone follows the best strategy, and there is a rolling merge in which traffic continues in the merging lane until there is a safe gap in the continuing lane (and there should always be a safe gap).  This is an System Optimal, SO, solution and has the highest capacity for the merging section.  (i.e. utilize the capacity in the ending lane as long as possible).   

What do people really do?  Each individual car will try to follow their own User Optimal, UO, strategy.  For some cars, that UO strategy will be to stay in the moving lane until the last minute and then force their way into the continuing lane, even when there is no safe gap.  To prevent this, all other cars can move into the continuing lane as soon as they see the merge notice, and ensure there is no safe gap and punish the last minute switchers, i.e. block their UO solution, by NOT letting them in.  What all cars adopt is called a Nash Equilibrium in that most cars will not follow yheir owb UO soluion, will block some from their UO solution, and will adopt a Nash Equilibrium instead. 

Traffic engineers are trained to believe that everyone will adopt the most efficient, SO, solution.  But individuals will see their own UO solution as the most efficient.  Unfortunately this leads to Nash Equilibriums, where individuals can block each other from that most efficient solution. They are called Nash Equilibriums because they were descrbed by mathematician John Nash, the subject of the movie, A Beautiful Mind. No one gets what they want. (The Blonde, if everyone goes after the Blonde, because they will block each other.)  Instead people will get what they need. (Nash Equilibriums).  https://www.youtube.com/watch?v=vCyZvfRHkC4