Correlated Equilibrium

Table $3$: Payoff Bimatrix

B$1$ B$2$ B$3$

A$1(3,3)(5,2)(3,5)$

A$2(8,4)(4,4)(3,1)$

A$3(4,5)(7,5)(4,3)$

$1)$ Check if the following distribution is a correlated equilibrium

Table $4$: Distribution over strategy profiles

B$1$ B$2$ B$3$

A$110\%10\%10\%$

A$210\%10\%20\%$

A$310\%10\%10\%$

$2)$ Write the linear program that finds the correlated equilibrium with the highest social welfare $($sum of

the players$$ payoffs$)$ Implement Matlab, Python or Julia code to find this correlated equilibrium.

Show your code in your submission

$3)$ Write the linear program that finds the correlated equilibrium that achieves the maxmin fairness

objective Implement Matlab, Python or Julia code to find this correlated equilibrium. Show your

code in your submission