Continuity and Equilibrium Stability

This paper discusses the problem of stability of equilibrium points in normal form games in the tremling-hand framework. An equilibrium point is called perffect if it is stable against at least one seqence of trembles approaching zero. A strictly perfect equilibrium point is stable against every such sequence. We give a sufficient condition for a Nash equilibrium point to be strictly perfect in terms of the primitive characteristics of the game (payoffs and strategies), which is new and not known in the literature. In particular, we show that continuity of the best response correspondence (which can be stated in terms of the primitives of the game) implies strict perfectness; we prove a number of other useful theorems regarding the structure of best responce correspondence in normal form games.Strictly perfect equilibrium, best responce correspondence, unit simplex, face of a unit simplex

A Refinement of Perfect Equilibria Based On Substitute Sequences

We propose an equilibrium refinement of strict perfect equilibrium for the finite normal form games, which is not known in the literature. Okada came up with the idea of strict perfect equilibrium by strengthening the main definition of a perfect equilibrium, due to Selten [14]. We consider the alternative (and equivalent) definition of perfect equilibrium, based on the substitute sequences, as appeared in Selten [14]. We show that by strengthening and modifiyng this definition slightly, one can obtain a refinement stronger than strict perfectness. We call the new refinement strict substitute perfect equilibrium. The main advantage of this solution concept is that it reflects the local dominance of an equilibrium point. An example is provided to show that a strict perfect equilibrium may fail to be strict substitute perfect.Perfect equilibrium, strictly perfect equilibrium, substitute sequence, substitute perfect equilibrium, unit simplex

Bilateral Matching with Latin Squares

We develop a general procedure to construct pairwise meeting processes characterized by two features. First, in each period the process maximizes the number of matches in the population. Second, over time agents meet everybody else exactly once. We call this type of meetings absolute strangers. Our methodological contribution to economics is to offer a simple procedure to construct a type of decentralized trading environments usually employed in both theoretical and experimental economics. In particular, we demonstrate how to make use of the mathematics of Latin squares to enrich the modeling of matching economies

THE CHEAPEST HEDGE:A PORTFOLIO DOMINANCE APPROACH

Investors often wish to insure themselves against the payoff of their portfolios falling below a certain value. One way of doing this is by purchasing an appropriate collection of traded securities. However, when the derivatives market is not complete, an investor who seeks portfolio insurance will also be interested in the cheapest hedge that is marketed. Such insurance will not exactly replicate the desired insured-payoff, but it is the cheapest that can be achieved using the market. Analytically, the problem of finding a cheapest insuring portfolio is a linear programming problem. The present paper provides an alternative portfolio dominance approach to solving the minimum-premium insurance portfolio problem. This affords remarkably rich and intuitive insights to determining and describing the minimum-premium insurance portfolios.

A Characterization of Compact-friendly Multiplication Operators

Answering in the affirmative a question posed in [Y.A.Abramovich, C.D.Aliprantis and O.Burkinshaw, Multiplication and compact-friendly operators, Positivity 1 (1997), 171--180], we prove that a positive multiplication operator on any $L_p$-space (resp. on a $C(\Omega)$-space) is compact-friendly if and only if the multiplier is constant on a set of positive measure (resp. on a non-empty open set). In the process of establishing this result, we also prove that any multiplication operator has a family of hyperinvariant bands -- a fact that does not seem to have appeared in the literature before. This provides useful information about the commutant of a multiplication operator.Comment: To appear in Indag. Math., 12 page

A Correspondence-Theoretic Approach to Dynamic Optimization

This paper introduces a method of optimization in infinite-horizon economies based on the theory of correspondences. The proposed approach allow us to study time-separable and non-time-separable dynamic economic models without resorting to fixed point theorems or transversality conditions. When our technique is applied to the standard time-separable model it provides an alternative and straightforward way to derive the common recursive formulation of these models by means of Bellman equations

Matching and Anonymity

This work introduces a rigorous set-theoretic foundation of deterministic bilateral matching processes and studies systematically their properties. In particular, it formalizes a link between matching and informational constraints by developing a notion of anonymity that is based on the agents\u27 matching histories. It also explains why and how various matching processes generate different degrees of informational isolation in the economy. We illustrate the usefulness of our approach to modeling matching frameworks by discussing the classical turnpike model of Townsend

Contagion Equilibria in a Monetary Model

This article explores the Monetary Models

Anonymous Markets and Monetary Trading

We study infinite-horizon monetary economies characterized by trading frictions that originate from random pairwise meetings, and commitment and enforcement limitations. We prove that introducing occasional trade in \u27centralized markets\u27 opens the door to an informal enforcement scheme that sustains a non-monetary efficient allocation. All is required is that trading partners be patient and their actions be observable. We then present a matching environment in which trade may occur in large markets and yet agents\u27 trading paths cross at most once. This allows the construction of models in which infinitely lived agents trade in competitive markets where money plays an essential role

A Random Matching Theory.

We develop the theoretical underpinnings of pairwise random matching mechanisms. We formalize the mechanics of matching, and study the links between properties of the different mechanisms and trade frictions. A particular emphasis is placed on providing exact mappings between matching technologies and informational constraints.Random matching ; frictions ; anonymous trading ; spatial intersections ; search