Analysis of Conflict

To all those who bleat consistently about the implausibility of the Nash equilibrium, here's some words from Roger Myerson (heavily edited):

"A solution concept can be viewed as a mapping that determines for every game a set of mathematical descriptions of how players should behave...The goal of game theoretic analysis is to generate a solution concept that has the following two properties:

(a) For each prediction in the solution set, there exist environments where this prediction would accurately prescribe how rational, intelligent players would behave.

(b) For any prediction not in the solution set, there is no environment where this prediction would be an accurate description of how rational, intelligent players would behave.

[Note: an environment consists of all those things not modeled in the game.]

Call any solution that satisfies (a) a lower solution, and that satisfies (b) an upper solution. Ideally we want a solution concept to be both an upper and lower solution, i.e. an exact solution.

This is hard to figure out in practice...a lower solution excludes all unreasonable predictions but may include some reasonable predictions, while an upper solution includes all reasonable predictions but may include some unreasonable predictions...it may be best to think of a Nash solution as an upper solution than an exact solution."

This is from Myerson's 1995 book "Game Theory: Analysis of Conflict". Better than any other text I've read by miles.

Incidentally, there's a curious symmetry between the idea of an exact solution as stated above (a) + (b) and the two "fundamental" welfare theorems. It would appear to suggest some deep connection between the "goal of game theoretic analysis" and the goal of resource allocation...I dunno....