If I know all Nash equilibria is it easy to claim I know all correlated ones (and can calculate them all easily, or put a symbolic expression that defines them)?
Let's assume a case 2 player games.
Can existence of Nash equilibria simplify discovery of all correlated equilibria?
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game-theory
nash-equilibrium
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1I haven't read the article, but the intro and references may help you: http://theory.stanford.edu/~tim/papers/cor.pdf – 2017-02-25
1 Answers
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The answer is no. (It is not clear whether your question concern strategy profiles or payoffs, so the following considers both interpretations.)
Consider $n$-player finite games. The set of correlated equilibria (strategy profiles) is convex and compact and is defined by a system of linear inequalities, which are easy to solve.
The set of correlated equilibria contains all the Nash equilibria. However, in general, the set of correlated equilibrium payoffs is a proper superset of the convex hull of the Nash equilibrium payoffs. Thus, identifying the Nash equilibrium payoffs would not tell you all that players can achieve.
Moreover, even it did, computing all Nash equilibria (strategy profiles) is computationally much harder than computing all correlated equilibrium (strategy profiles).
About correlated equilibrium, I recommend reading Chapter 8 from Game Theory by Maschler, Solan, Zamir (2013).