Kim C. Border

Samurai Accountant: A Theory of Auditing and Plunder

A risk neutral principal wishes to exact a payment from a risk neutral agent whose wealth he does not know, but may verify through a costly auditing procedure. We characterize efficient schemes for the principal when he is allowed to choose schedules for preaudit and postaudit payments and audit probabilities, subject to the constraint that only monetary incentives can be used and that the principal may never make a net payment to the agent. The main results are that efficient schemes involve preaudit payments which are increasing in the agents wealth, audit probabilities are decreasing in the agents wealth and also satisfy certain constraints as equalities. In general, such schemes involve stochastic auditing and rebates after an audit.

Social welfare functions for economic environments with and without the pareto principle

It is shown for the case of private goods economies that every social welfare function satisfying a weak nonimposition condition and the independence of irrelevant alternatives axiom is of one of the following forms. It is either null, or the class of decisive coalitions is an ultrafilter, or the class of anti-decisive coalitions is an ultrafilter. In the case of a private goods economy with finitely many traders, the latter conditions imply the existence of either a dictator or anti-dictator. By requiring the Pareto principle as well, it is easily seen that the social welfare function must be dictatorial.

Preferences over Solutions to the Bargaining Problem

There are several solutions to the Nash bargaining problem in the literature. Since various authors have expressed preferences for one solution over another, we find it useful to study preferences over solutions in their own right. We identify a set of appealing axioms on such preferences that lead to unanimity in the choice of solution, which turns out to be the solution of Nash.

L p -spaces

In this chapter, we introduce the classical L p -spaces and study their basic properties. For a measure space (X, Σ, μ) and 0 < p <∞, the space L p (μ) is the collection of all equivalence classes of measurable functions f for which the p-norm

More on Harsanyi's Utilitarian Cardinal Welfare Theorem

{\left\| f \right\|_p} = \left( {\int {{{\left| f \right|}^p}d{\mu ^{\frac{1}{p}}}} } \right) < \infty .

Functional Analytic Tools for Expected Utility Theory

Abstract This paper shows that a choice function is either consistent with the expected utility hypothesis or is ex ante dominated for some prior.

Riesz Representation Theorems

If individuals and society both obey the expected utility hypothesis and social alternatives are uncertain, then the social utility must be a linear combination of the individual utilities, provided the society is indifferent when all its members are. This result was first proven by Harsanyi [4] who made implicit assumptions in the proof not actually needed for the result (see [5]). This note presents a straightforward proof of Harsanyis theorem based on a separating hyperplane argument.