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From my (mathematician's) perspective, when the solution to the optimal transportation problem corresponds to a Nash equilibrium, this is called a Cournot-Nash
by micwawa 11y ago
From my (mathematician's) perspective, when the solution to the optimal transportation problem corresponds to a Nash equilibrium, this is called a Cournot-Nash equilibrium. This does not happen generically.
In other words, it is very unlikely to simultaneously minimize both the expected commute cost for the group and for each individual.
However, in the continuous case, you can fix this using taxes, tolls or incentives (in theory - in practice I don't know. )
Blanchet and Carlier have some nice mathematical articles including
https://www.ceremade.dauphine.fr/~carlier/blanchetcarlierfinal.pdf https://www.ceremade.dauphine.fr/~carlier/blanchetcarlierfin...
- alimw 11y agoAre you saying that an equilibrium is Cournot-Nash if it does manage to "simultaneously minimize both the expected commute cost for the group and for each individual"? Not sure that's right...
- micwawa 11y agoIn the literature I've encountered a Cournot-Nash Equilibrium is a solution to an optimal transportation problem. There could be some discrepancies in definitions as to the parameters one is allowed to vary. This is also assumed to be a global minimum - not just local.
- alimw 11y agoIn the paper you reference, an 'optimal transport' problem does indeed arise in connection with Cournot-Nash equilibrium. However the naming is a coincidence, it is unrelated to the problem of finding the most efficient routing of traffic. Think rather 'earth-moving'. https://en.wikipedia.org/wiki/Earth_mover%27s_distance https://en.wikipedia.org/wiki/Earth_mover%27s_distance The paper does however note the traffic problem in passing: "the variational approach we develop presents some similarities with the variational approach to Wardrop equilibria on congested networks and in both cases equilibria are socially inefficient."
- micwawa 11y agoThe 'optimal transportation' is misleading in this case : People are not interchangeable, so you are actually trying to find a map between the space of { people who have to go places } and {routes they might take } . Once everybody has chosen a route, there is a measure on the space of routes. The cost of each route to each person depends on the measure on the route space. Once you have this pairing of measures, you can ask if it's optimal or not.
- alimw 11y agoI think we agree :) Thanks for the reference btw, I'm supposed to be writing my thesis on such things.