## Pareto Optimality

Although not discussed in depth in class, upon supplementing my learning with edX I became interested in examples where the Nash Equilibrium does not represent the only, or even the logical optimal solution. Professor Tardos discusses tolls, and creates an example where the a path equal to x/10 minutes (x being amount of people taking path) and a path at a fixed value of 50 minutes start and end at the same position. As there are 500 people, if all of them go down either one of the paths, it will take 50 minutes. But, if they split between the paths, 250 of them could take 25 minutes while the others take 50. This allows the average overall travel time to be minimized, but with the mentality of questioning whether switching paths will speed up a individuals travel, that could not be called equilibrium. At this, tolls were discussed. Researching this type of situation more, also brought up another idea of optimality/equilibrium, called Pareto Equilibrium.

To quote the article/discussion forum, ”

Nash equilibrium is an outcome in which every player is doing the best he possibly can given other players’ choices. So, no player can benefit from unilaterally changing his choice.

Pareto optimal is an outcome from which any attempt to benefit someone by deviating to some other outcome will necessarily result in a loss in satisfaction to someone else.”

Like the Nash equilibrium, multiple points of Pareto optimal can exist on the same hypothetical. It offers an interesting alternative to more properly model situations depending on the actual conditions. Just as we also explored an example in game theory (matrix form) where the punishment of the other player factored in positively, this hits the other side of the spectrum, accounting for a more altruistic approach to game theory and traffic congestion problems.

https://www.quora.com/What-is-the-difference-between-Nash-Equilibrium-and-Pareto-Optimality