Inquiry to: categories list-serve subscribers In the mid- to late 70s there were meetings at Columbia University in New York of mathematicians interested in topos theory, which meetings I attended as a student of Peter Freyd. At one such meeting, someone proposed and solved the following problem, which I have since named The Manhattan Street Problem. (Note: it was NOT so named at the time.) Consider a large number of commuters, all traveling from south to north along two parallel highways. Connecting the two north-south highways are one (or more?) east-west linking streets, all of which are one way from west to east. The speed at which a commuter moves along any highway or street is a function of the number of users on that (part of that) highway or street, e.g., as more commuters who are initially on the western of the two north-south highways choose to leave and go over to the eastern of the two north-south highways, the speed of traffic on the western highway increases and the speed on the eastern highway decreases. The functions relating speed to number of users are not (necessarily) the same for each highway or street. (I think, however, that the most elegant solution would have a single function applicable to both highways and (all) street(s).) Each commuter chooses whether (and when, if there's more than one cross over street) to go over to the eastern highway in an attempt to minimize individual total travel time. Problem: Specify the speed controlling function(s), the number of crossing east-west roads and, if necessary, the distances, e.g., distance between eastern and western highways as a fraction of total north-south distance, or distance between various east-west roads, again presumably as a fraction of total north-south distance, such that: the system stabilizes, i.e., individual commuters cannot improve their time by changing their route, BUT the total travel time summed over all travelers is NOT a minimum. Thus, if such a solution is found, an omniscient, big brother traffic controller, by (randomly?) requiring some commuters to take a route slower than what he/she would individually choose, could thereby decrease (minimize?) travel time (hence air pollution?) for the whole commuting community. Plausibility argument that this might be possible: That the situation stabilizes seems intuitively plausible to me. That the stable situation might not minimize total travel time is suggested by the following: If the big brother traffic controller moves an individual from a too heavily traveled highway, the benefit flows to a large number of commuters left behind on that highway, which flows faster, even though the moved individual may be shunted over to a route slower for that individual. If anyone: a) remembers who presented and solved this problem at Columbia, or b) remembers the solution, or c) can point me toward where this might be solved in the literature, or d) can provide any other help, I would be extremely grateful. Samuel Johnson (sjohnson@mail.sjcsf.edu) Postscript: A solution would have (obvious?) implications for those who have great faith in the general applicability of free market mechanisms and Adam Smith's invisible hand for solving problems or finding best strategies from a society's point of view.