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

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.

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

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

An Overlapping Generations Model Core Equivalence Theorem

The classical Debreu-Scarf core equivalence theorem asserts that in an exchange economy with a finite number of agents art allocation (under certain conditions) is a Walrasian equilibrium if and only if it belongs to the core of every replica of the exchange economy. The pioneering work of P. Samuelson has shown that such a result fails to be true in exchange economies with a countable number of agents. This paper presents a Debreu-Scarf type core equivalence theorem for the overlapping generations (OLG) model. Specifically, the notion of a short-term core allocation for the overlapping generations model is introduced and it is shown that (under some appropriate conditions) an OLG model allocation is a Walrasian equilibrium if and only if it belongs to the short-term core of every replica of the OLG economy

When is the Core Equivalence Theorem Valid?

In 1983 L. E. Jones exhibited a surprising example of a weakly Pareto optimal allocation in a two consumer pure exchange economy that failed to be supported by prices. In this example the price space is not a vector lattice (Riesz space). Inspired by Jones' example, A. Mas-Colell and S. F. Richard proved that this pathological phenomenon cannot happen when the price space is a vector lattice. In particular, they established that (under certain conditions) in a pure exchange economy the lattice structure of the price space is sufficient to guarantee the supportability of weakly Pareto optimal allocations by prices-i.e., they showed that the second welfare theorem holds true in an exchange economy whose price space is a vector lattice. In addition, C. D. Aliprantis, D. J. Brown and O. Burkinshaw have shown that when the price space of an exchange economy is a certain vector lattice, the Debreu-Scarf core equivalence theorem holds true, i.e., the sets of Walrasian equilibria and Edgeworth equilibria coincide. (An Edgeworth equilibrium is an allocation that belongs to the core of every replica economy of the original economy.) In other words, the lattice structure of the price space is a sufficient condition for avoiding the pathological situation occurring in Jones' example. This work shows that the lattice structure of the price space is also a necessary condition. That is, "optimum" allocations in an exchange economy are supported by prices (if and) only if the price space is a vector lattice. Specifically, the following converse-type result of the Debreu-Scarf core equivalence theorem is established: If in a pure exchange economy every Edgeworth equilibrium is supported by prices, then the price space is necessarily a vector lattice

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