Talk:Correlated equilibrium

Incomplete Definition?

The formal definition section says that a correlated equilibrium is the combination of a countable probability space and an information partition. Isn't that missing the strategy? Where is the mapping from the sample space to the action set?

Bayesiangame (talk) 21:14, 13 February 2017 (UTC)

Proposed additions

• Perhaps it would be helpful to have an example where the two agents would deviate from the strategy proposed by the random variable?
• Also, does the value of the random variable have to prescribe a strategy? Couldn't it be any type of value, like the flip of a coin?
  • Actually, I see now that it follows from the formal definition that there has to be some correlation in the probability distribution between the agent's chosen strategy and every other agent's chosen strategy.

• Wouldn't it help, when giving the three Nash equilibria for the Chicken game, to also give the expected payoffs they lead to? PhS (talk) 11:49, 31 August 2017 (UTC)

• I'm no specialist but it seems that correlated equilibria are more general than Nash equilibria, and they allow higher payoffs. If correct, this should be stated in the article. PhS (talk) 11:52, 31 August 2017 (UTC)

nybbles 07:35, 19 July 2007 (UTC)

typo in [1]

The list of references says "Tardos, Eva (2004) Class notes from Algorithmic game theory (note an important typo)". I guess the typo is in formula (1), where the range of the right hand sum should be equal to the one on the left hand sum? Maybe it'd be helpful to further specify the typo's location in the article, I don't know the usual practice in that case on Wikipedia.

84.238.56.25 (talk) 12:50, 15 July 2008 (UTC)

alternative formulation

I find the formal definition here very non-intuitive. I'd like to suggest the following, which I think is more intuitive but mathematically equivalent.

$\displaystyle \sum _{\omega \in \Omega }q_{i}(\omega )u_{i}(s_{i},s_{-i})=\max _{\phi }\sum _{\omega \in \Omega }q_{i}(\omega )u_{i}(\phi (s_{i}),s_{-i})$

We know that the constant-selection of $\phi (s_{i})=s_{i}$ is in the set of all selection rules, so the right-side must be atleast as large as the left-side. Equality must hold if this is really the best strategy. This is better than the current formulation because it makes it clear to the reader that we are varying over all possible $\phi$. The $\max$ can be switched to $\sup$ if desired, but $\max$ is easily understood by the lay reader without an analysis background.

generality

The first paragraph says that correlated equilibria are more general than Nash equilibria. I'd like some more explanation.