The standard ex post type of collusion is a supervisor-agent agreement to misrepresent the outcome of supervision. Under ex ante collusion the agent makes a side transfer to the supervisor, who, in return, stops monitoring the agent's productivity. Extending Tirole's [1986] model of hierarchy to...

Abstract This paper shows that the core outcomes of the assignment game coincides with the set of fixed points of a certain function. The lattice property of the core, as well as its non-emptiness, are proved using Tarski's fixed point theorem.