3 ms·

This applies even with perfect information, as long as drivers are completely selfish.

lvh 10y ago
How's that work? Is the idea that an individual driver would have to take a penalty in order for everyone else to have better road use? (Also, is this specified somewhere? It seems like the paradox relies on people making their minds up ahead of time (hence imperfect information) and then not changing their minds halfway.)
- saosebastiao 10y ago
  Exactly. In other words, in order to globally optimize for throughput, you would have to deoptimize some people's routes.
  - snrplfth 10y ago
    Normally you would do this through prices, but most roads don't work that way.
    - trvlngsalesmn 10y ago
      Hwy 635 in Dallas has a variable-toll expressway lower level.
      - snrplfth 10y ago
        There are definitely many variable-tolled roads. The trouble is that frequently they are embedded in a system of non-tolled (or, really, not-allowed-to-be-tolled) roads, and that the tolling is not well-focused on congestion. Basically, the Braess "paradox" emerges if you try to make a road network that's optimal for travel patterns over an entire day, without using pricing to ration scarce space.
  - caf 10y ago
    In the toy example given in the linked page, with the A->B link in place the global optimum (in terms of total minutes spent travelling) is for 1750 cars to travel Start->A->End for 67.5 minutes of travel, 500 cars to travel Start->A->B->End for 45 minutes of travel and 1750 cars to travel Start->B->End for 67.5 minutes of travel. This gives a total of 258750 minutes spent travelling. If you imagine that one of the Start->A->End travellers switches to Start->A->B->End, we now have 1749 cars travelling Start->A->End for 67.5 minutes, 501 cars travelling Start->A->B->End for 45.01 minutes and 1750 cars travelling Start->B->End for 67.51 minutes. The car that switched improved its own travel time from 67.5 minutes to 45.01 minutes, but the total time spent travelling increased to 258750.01 minutes (one driver saved themselves 22.49 minutes, but cost 2250 other drivers 0.01 minutes each). So yes, if you found yourself in that second state, to improve the global optimum you would have to move to the first state by de-optimising the route of one of those 501 Start->A->B->End drivers.
- ThrustVectoring 10y ago
  Having every driver take the shortest path for them is not the same thing as minimizing total transit time for all drivers. Similarly with some of the other tragedy-of-the-commons situations, having each fisher maximize the number of fish they catch is not the same thing as maximizing the total number of fish caught by all fishers.
- rawnlq 10y ago
  The prisoner's dilemma linked to in the article is usually the go-to demo since it only has 4 outcomes. The nash equilibrium would be for both prisoners to deflect but this is worse than if they both stayed silent. Both staying silent is not an equilibrium because if one of them decides to be selfish and cheat, he can do better for himself. Basically the information you need is agreement/cooperation ahead of time to know that neither side will cheat just to do slightly better for himself at the cost of others.

lvh 10y ago

How's that work? Is the idea that an individual driver would have to take a penalty in order for everyone else to have better road use? (Also, is this specified somewhere? It seems like the paradox relies on people making their minds up ahead of time (hence imperfect information) and then not changing their minds halfway.)

saosebastiao 10y ago
Exactly. In other words, in order to globally optimize for throughput, you would have to deoptimize some people's routes.
- snrplfth 10y ago
  Normally you would do this through prices, but most roads don't work that way.
  - trvlngsalesmn 10y ago
    Hwy 635 in Dallas has a variable-toll expressway lower level.
    - snrplfth 10y ago
      There are definitely many variable-tolled roads. The trouble is that frequently they are embedded in a system of non-tolled (or, really, not-allowed-to-be-tolled) roads, and that the tolling is not well-focused on congestion. Basically, the Braess "paradox" emerges if you try to make a road network that's optimal for travel patterns over an entire day, without using pricing to ration scarce space.
- caf 10y ago
  In the toy example given in the linked page, with the A->B link in place the global optimum (in terms of total minutes spent travelling) is for 1750 cars to travel Start->A->End for 67.5 minutes of travel, 500 cars to travel Start->A->B->End for 45 minutes of travel and 1750 cars to travel Start->B->End for 67.5 minutes of travel. This gives a total of 258750 minutes spent travelling. If you imagine that one of the Start->A->End travellers switches to Start->A->B->End, we now have 1749 cars travelling Start->A->End for 67.5 minutes, 501 cars travelling Start->A->B->End for 45.01 minutes and 1750 cars travelling Start->B->End for 67.51 minutes. The car that switched improved its own travel time from 67.5 minutes to 45.01 minutes, but the total time spent travelling increased to 258750.01 minutes (one driver saved themselves 22.49 minutes, but cost 2250 other drivers 0.01 minutes each). So yes, if you found yourself in that second state, to improve the global optimum you would have to move to the first state by de-optimising the route of one of those 501 Start->A->B->End drivers.
ThrustVectoring 10y ago
Having every driver take the shortest path for them is not the same thing as minimizing total transit time for all drivers. Similarly with some of the other tragedy-of-the-commons situations, having each fisher maximize the number of fish they catch is not the same thing as maximizing the total number of fish caught by all fishers.
rawnlq 10y ago
The prisoner's dilemma linked to in the article is usually the go-to demo since it only has 4 outcomes. The nash equilibrium would be for both prisoners to deflect but this is worse than if they both stayed silent. Both staying silent is not an equilibrium because if one of them decides to be selfish and cheat, he can do better for himself. Basically the information you need is agreement/cooperation ahead of time to know that neither side will cheat just to do slightly better for himself at the cost of others.