What is meant by 'Correlated action recommendation' in Correlated equilibrium?

Question

I have come across the definition of Correlated equilibrium in Game theory, where there is a trusted advisor, who provides players with recommendations on what to play. I understand, what makes correlated equilibrium an equilibrium. However, it is not clear to me, what exactly is meant by correlated action recommendations. Could anyone provide an example, or elaborate on in what way can recommendations be correlated?

Answer 1

One example comes from the Bach or Stravinsky game, BoS. Which concert will the couple go to when they can't communicate? There are three Nash equilibria, They both go to Bach, they both go to Stravinsky, or the mixed strategy, where they (independently) randomize (and hence sometimes end up at different concerts). The additional correlated equilibrium is where they observe a public coin toss (say, if the last digit on the DJIA is odd or even), and go to Bach if it is heads and Stravinsky if it is tails. Their actions are correlated with each other, and hence the name. In other games, the signals don't have to be perfectly correlated with each other. Some cool examples and precise definitions in Osborne and Rubinstein.