“All-Way Stops”, 2023-01-27 ():
Using economic incentives analysis, we demonstrate substantial implications from tweaking the familiar practice in the United States and many other countries of erecting one stop sign in each direction to ensure orderly passing at crossroads.
We point out that the existing mechanism does not permit a Nash equilibrium for all drivers to abide by, and prove that erecting one fewer sign (eg. only 3 stop signs at a 4-way crossroad) does. Not only is the simpler mechanism self-enforcing, but its resulting equilibrium outcome also enjoys substantial economic gains.
For example, for fuel gas savings alone, the new mechanism is estimated to reduce 0.5 months of gas consumption every year, let alone savings in drivers’ time, infrastructure costs, carbon/pollutants emissions, and police expenditure.
[Keywords: carbon emission, ESG, infrastructure spending, game theory, mechanism design, Nash equilibrium, police funding, traffic rules]
…Despite its popularity in many countries such as the United States, Canada, Mexico, South Africa, Liberia, etc., the all-way stop sign mechanism has not been adopted globally…The existing mechanism is so widely adopted that few people ever doubt whether it is efficient—except that it is not. Furthermore, this mechanism is not even incentive compatible. Intuitively, assuming that drivers get a disutility from stopping their moving vehicles but they also do want to avoid collisions, then it is not a Nash equilibrium for drivers in all directions to abide by their respective stop signs: As a profitable deviation, if you believe that all other drivers will stop at the crossroads and observe the traffic before moving again, you know that you can avoid collisions even if you just run the stop sign. Then under the usual rationality assumption for economic agents, how can we expect a selfish driver, who does not care about the angry curses from drivers in the other directions, to ever abide by the stop-sign rule at all? Indeed, with 4 stop signs in each direction, we prove that any Nash equilibrium always features some drivers running the stop sign!
…Instead of erecting one stop sign in every direction of a crossroads, we consider simply removing one sign—any one, and allowing vehicles in that direction to pass without stopping. We prove that under this new mechanism, it is indeed a unique Nash equilibrium for all drivers in the remaining directions with stop signs to abide by the traffic rule, as their cost (chance of collision) of running the stop sign increases. In this equilibrium, no police monitoring is ever needed (so police funding could be put in more efficient alternative uses).
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