Competitive Selling Mechanisms: the Delegation Principle and Farsighted Stability.

We analyze the problem of competitive mechanism design within the context of a model of product differentiated oligopoly. In an oligopoly setting, participation by an agent in any one firm's catalog is endogenously determined. This facts leads naturally to a modification of the classical notion of incentive compatibility for mechanisms. We extend the classical notion of incentive compatibility to take into account endogenous participation, introducing the notion of participation incentive compatibility (PIC). Our mains contribution is a characterization of all PIC selling mechanisms in terms of catalogs. In particular, we show that a selling mechanism is PIC if and only if there exists a unique, minimal catalog profile which implements the mechanisms. We call this characterization the delegation principle.