Agency Spaces
by
Zivan Forshner
University of Haifa

ABSTRACT The plausibility of contract theory as a mode of behavior for rational entities, is studied from a general equilibrium point of view on a class of problems that the theory solves. The generic problem of the class being considered, is the celebrated problem of selling one unit of an, indivisible, object. The principal is viewed as a Stackelberg leader (hereafter Stackelberg-principal) that her choice variable is a mechanism. Contract theory is founded on two axioms: (a) Every principal-agent problem is solved independently of the solution contract theory assigns to other principal-agent problems; (b) There are no a-priori restrictions on the domain of principal-agent problems being solved. These axioms allow the consideration of a large collection of such principal-agent problems, each one being solved independently according the Bayesian-Nash equilibrium paradigm. The collection of principal-agent problems and the principal’s payoffs associated with such equilibria can be conveniently represented by a certain correspondence termed the Bayesian-Nash Equilibrium Expected Payoff (BNEEP) correspondence.

Within the above setting, the interest here is in two central issues. The first task is to identify a large collection of principal-agent problems of selling one unit of an object, over which contract theory operator (i.e. setting an optimal mechanism) can be applied to without forming inconsistencies. The second task is to understand the way the operator is applied without forming inconsistencies. It is first argued that applying - without any restrictions on a universal domain - contract theory operator, leads to inconsistencies. The logical conclusion is that if we seek to avoid inconsistencies, the domain of problems for which we apply the operator must be restricted. The fact that some principal-agent problems are related via different usage's of Bayes rule, imply two important consequences. The first is that such problems must be solved simultaneously and not independently. The second is that any problem included in the domain implies that other problems must be excluded from the domain. These observations lead to the necessity to apply a general equilibrium approach to the BNEEP correspondence.

Both contract theory and implementation theory, have considered (implicitly) the BNEEP correspondence. The fact that each one of these theories took a pointwise (discrete) approach to each incomplete information problem in the domain of the BNEEP correspondence, raises interest in the topological properties of the BNEEP correspondence and particularly continuity. Study of continuity requires a specification of topological structure on the space of principal-agent problems. A hard conceptual problem in specifying any topological structure, arises from the fact that any topological structure is affected from equilibrium considerations. This means that one cannot assume a topology, but has to deduce it - at least at certain problems - from equilibrium considerations. Thus the following natural question arises: Is it the case that on a sufficiently large collection of principal-agent problems, the topology and the domain are actually determined from equilibrium considerations?

It turns out that the conjecture regarding the determinacy of topology and domain is correct. A structure that enables us to solve for the topology on the space of principal-agent problems is introduced. A domain of principal-agent problems over which contract theory operator can be applied without forming inconsistencies is characterized. A unified solution for principal-agent problems belonging to our domain is defined. The solution uses the single axiom of consistency. Further properties of the solution are studied and the possibility to support the consistent solution with a maximization behavior on the principal’s part is investigated.

Date received: April 24, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caez-33.