Wednesday, June 09, 2004
How Free Choices May Lead to a Non-Optimal Equilibrium
Consider a beach serviced by two ice cream vans, A and B. If we imagine that the beach contains a continuum of people, evenly spaced along it and that people will always go to their nearest vendor then the optimal places for the ice cream vans to be positioned are at one quarter and three quarters of the way along the beach. In this way will the sum of the distances from each person to a van be minimised. This is shown by the diagram below:
----------A--------------------B----------
However, in this situation it will be in A's interest to move a little to the right. By doing so they will eat into B's share while preserving their own. Although the people on the far left will have to walk further for refreshment, they will still go to A over B. Similarly, B will try and take some of A's business by moving a little to the left.
-------------A--------------B-------------
This process will continue until there is no further advantage to be had. In other words, when they are beside each other:
--------------------AB--------------------
This is the only position which will provide an equilibrium, ie, where there will be no incentive to change. Without an iron fisted local authority, the kind so lacking in Amity (Jaws, 1975), the only winners will be the ice cream vans.
Make of this what you will.
|
Consider a beach serviced by two ice cream vans, A and B. If we imagine that the beach contains a continuum of people, evenly spaced along it and that people will always go to their nearest vendor then the optimal places for the ice cream vans to be positioned are at one quarter and three quarters of the way along the beach. In this way will the sum of the distances from each person to a van be minimised. This is shown by the diagram below:
----------A--------------------B----------
However, in this situation it will be in A's interest to move a little to the right. By doing so they will eat into B's share while preserving their own. Although the people on the far left will have to walk further for refreshment, they will still go to A over B. Similarly, B will try and take some of A's business by moving a little to the left.
-------------A--------------B-------------
This process will continue until there is no further advantage to be had. In other words, when they are beside each other:
--------------------AB--------------------
This is the only position which will provide an equilibrium, ie, where there will be no incentive to change. Without an iron fisted local authority, the kind so lacking in Amity (Jaws, 1975), the only winners will be the ice cream vans.
Make of this what you will.
|
