A Theoretical Foundation for Bilateral Matching Mechanisms

This work introduces a rigorous set-theoretic foundation of bilateral matching mechanisms and studies their properties in a systematic manner. By providing a unified framework to study ilateral matching mechanisms, we formalize how different spatial/informational constraints can be implemented via a careful selection of matching mechanisms. In particular, this paper explains why and how various matching mechanisms generate different degrees of information isolation in the economyspatial interactions, matching, information frictions

Interior Optima and the Inada Conditions

We present a new proof of the interiority of the policy function based on the Inada conditions. It is based on supporting properties of concave functions.growth model ; Inada conditions ; policy function

Monetary Equilibrium and the Differentiability of the Value Function

In this study we offer a new approach to proving the differentiability of the value function, which complements and extends the literature on dynamic programming. This result is then applied to the analysis of equilibrium in the recent class of monetary economies developed in [13]. For this type of environments we demonstrate that the value function is differentiable and this guarantees that the marginal value of money balances is well defined.value function ; optimal plans ; money

Invariant Subspaces of Operators on lp-Spaces

AbstractWhile the algebra of infinite matrices is more or less reasonable, the analysis is not. Questions about norms and spectra are likely to be recalcitrant. Each of the few answers that is known is considered a respectable mathematical accomplishment.P.R. Halmos [3, p. 24]A continuous operator T: X → X on a Banach space is quasinilpotent at a pointx0 whenever limn→∞||Tnx0||1/n = 0. Several results on the existence of invariant subspaces of operators which act on lp-spaces and are quasinilpotent at a non-zero point are obtained. For instance, it is shown that if an infinite positive matrix A = [aij] defines a continuous operator on an lp-space (1 ≤ p < ∞) and A is quasinilpotent at a positive vector, then for any bounded double sequence of complex numbers {wij: i,j = 1, 2, ... } the operator defined by the weighted infinite matrix [wijaij] has a non-trivial complemented invariant closed subspace

A Theoretical Foundation for Bilateral Matching Mechanisms.

This work introduces a rigorous set-theoretic foundation of bilateral matching mechanisms and studies their properties in a systematic manner. By providing a unified framework to study bilateral matching mechanisms, we formalize how different spatial/informational constraints can be implemented via a careful selection of matching mechanisms. In particular, this paper explains why and how various matching mechanisms generate different degrees of information isolation in the economy.Bilateral matching ; Frictions ; Anonymous trading ; Spatial interactions

An Elementary Proof of Douglas′ Theorem on Contractive Projections on L1-Spaces

AbstractDouglas (Pacific J. Math.15 (1965), 443-462) has shown that the conditional expectation operators are the only contractive projections on L1(σ) that leave the constant functions invariant. This remarkable result has applications to several areas and our objective is to present here an elementary and self-contained proof. Douglas* theorem has been proven and generalized in various contexts by many authors; for details see Ando (Pacific J. Math.17 (1966), 391-405), Bernau and Lacey (Pacific J. Math.53 (1974), 21-41), and Dodds et al. (Pacific J. Math.141 (1990), 55-77) and the references therein

On dominant contractions and a generalization of the zero-two law

Zaharopol proved the following result: let T,S:L^1(X,{\cf},\m)\to L^1(X,{\cf},\m) be two positive contractions such that $T\leq S$. If $\|S-T\|<1$ then $\|S^n-T^n\|<1$ for all n\in\bn. In the present paper we generalize this result to multi-parameter contractions acting on $L^1$. As an application of that result we prove a generalization of the "zero-two" law.Comment: 10 page

The Non-Archimedean Theory of Discrete Systems

In the paper, we study behavior of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behavior of the system w.r.t. variety of word transformations performed by the system: We call a system completely transitive if, given arbitrary pair $a,b$ of finite words that have equal lengths, the system $\mathfrak A$, while evolution during (discrete) time, at a certain moment transforms $a$ into $b$. To every system $\mathfrak A$, we put into a correspondence a family $\mathcal F_{\mathfrak A}$ of continuous maps of a suitable non-Archimedean metric space and show that the system is completely transitive if and only if the family $\mathcal F_{\mathfrak A}$ is ergodic w.r.t. the Haar measure; then we find easy-to-verify conditions the system must satisfy to be completely transitive. The theory can be applied to analyze behavior of straight-line computer programs (in particular, pseudo-random number generators that are used in cryptography and simulations) since basic CPU instructions (both numerical and logical) can be considered as continuous maps of a (non-Archimedean) metric space $\mathbb Z_2$ of 2-adic integers.Comment: The extended version of the talk given at MACIS-201