On the Irrelevance of Collusion in Perfectly Correlated Environments

I study a class of agency problems that are characterized by the existence of an underlying organizational hierarchy. Specifically, I analyze a two forked, three tiered hierarchy and I show that when the private information of the players in the second and in the third tiers of the hierarchy, across the two forks of the hierarchy is perfectly correlated, collusion by the players notwithstanding, the principal can always implement the full information optimum in a Bayes-Nash equilibrium