Competitive Selling Mechanisms: the Delegation Principle 
and Farsighted Stability

By

Frank H. Page, Jr.
Department of Finance
University of Alabama
Tuscaloosa, AL 35487
USA
phone: (205) 348-6097
FAX: (205) 348-0590
E-mail: fpage@cba.ua.edu


Abstract
We analyze the problem of competitive mechanism design within the context 
of a model of product differentiated oligopoly. In our model, firms compete 
via their catalogs, that is, via the sets of products (broadly defined) and 
prices firms offer to the market (i.e., catalogs are the primitives, while 
selling mechanisms are derived). In an oligopoly setting, participation by 
an agent in any one firm's catalog is endogenously determined. This fact 
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 main 
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 (Theorem 4).
Using the delegation principle, we conclude that in order to solve the 
problem of competitive mechanism design, an essentially cooperative problem, 
it is sufficient to consider only the underlying noncooperative problem of 
catalog choice by firms. Moreover, using the delegation principle we show 
that corresponding to each PIC mechanism there is a unique profile of 
nonlinear pricing schedules which implements the mechanism - thus, extending 
the taxation principle to problems of competitive nonlinear pricing (Theorem 5).
A second contribution is our application of the notion of farsighted 
stability to the problem of competitive mechanism design. We show that for 
any approximating finite subgame (of catalog choice), the farsightedly stable 
set of catalog profiles (and hence the farsightedly stable set of nonlinear 
pricing schedules) is nonempty (Theorem 10).