Is there a systematic way to calculate a correlated equilibrium? (in game theory)

Question

Consider the following game:

The pure Nash eq. are $( x_1,y_2 )$ and $( y_1,x_2 )$.

Now, in a correlated equilibria situation, you want to assign a probably of zero to playing $( y_1,y_2 )$.

So effectively choosing $p_1$ and $p_2$ in $U = 7 \cdot p_1 + 7 \cdot p_2 + 8 \cdot (1-p_1-p_2) = 8 - p_1-p_2$ to maximise $U$ but such that they are strictly positive.

But it is a constrained optimisation, but how do I work out what the constraints are?

Answer 1

Check out this paper on Correlated Equilibrium

Correlated-Q Learning

Amy Greenwald and Keith Hall

https://www.aaai.org/Papers/ICML/2003/ICML03-034.pdf