Existence Of Equilibrium Prices Research Articles

On the Equilibrium Without Loss in the Discrete Time Models of Economic Dynamics

The model of economic dynamics with a fixed budget is considered. The conditions are derived under which the model with a fixed budget has an equilibrium state with the equilibrium prices. The necessary and sufficient conditions for the existence of equilibrium prices are found.

Analyses of location-price game on networks with stochastic customer behavior and its heuristic algorithm

In this paper, a two-stage model is developed to investigate the location strategy and the commodity pricing strategy for a retail firm that wants to enter a spatial market with multiple competitive facilities, where a competitor firm is already operating as a monopoly with several outlets. Expected market shares are calculated based on the stochastic customer behavior on networks. The authors provide a sufficient condition for the existence of equilibrium prices in the price game for the first time. The existence and uniqueness of the pure strategy Nash equilibrium price with a specified utility function are proved in the subgame. A metaheuristic based on tabu search is proposed to search the optimal location-price solution of the model. In addition, the authors provide two numerical examples to illustrate how to obtain the optimal solution and conduct sensitivity analysis. The analysis shows that the best location decision is robust for the follower firm, price game is more intense when incomes of consumers are lower or there are more substitution products, and neither chain retail gains from the price competition.

Microeconomics-based resource allocation in overlay networks by using non-strategic behavior modeling

Behavior modeling has recently been investigated for designing self-organizing mechanisms in the context of communication networks in order to exploit the natural selfishness of the users with the goal of maximizing the overall utility. In strategic behavior modeling, the users of the network are assumed to be game players who seek to maximize their utility with taking into account the decisions that the other players might make. The essential difference between the aforementioned researches and this work is that it incorporates the non-strategic decisions in order to design the mechanism for the overlay network. In this solution concept, the decisions that a peer might make does not affect the actions of the other peers at all. The theory of consumer-firm developed in microeconomics is a model of the non-strategic behavior that we have adopted in our research. Based on it, we have presented distributed algorithms for peers’ “joining” and “leaving” operations. We have modeled the overlay network as a competitive economy in which the content provided by an origin server can be viewed as commodity and the origin server and the peers who multicast the content to their downside are considered as the firms. On the other hand, due to the dual role of the peers in the overlay network, they can be considered as the consumers as well. On joining to the overlay economy, each peer is provided with an income and tries to get hold of the service regardless to the behavior of the other peers. We have designed the scalable algorithms in such a way that the existence of equilibrium price (known as Walrasian equilibrium price) is guaranteed.

Market Equilibria in Fisher’s Model for Concave Economic Environments

Eisenberg and Gale [1959] showed that market equilibrium in Fisher’s model with linear utility functions could be obtained by maximizing a concave objective function subject to linear constraints. Eisenberg [1961] generalized this result to concave and linearly homogeneous functions. Eisenberg’s result can be used to establish that market equilibrium in economic environments where utility functions are homogeneous of arbitrary degree can be obtained by maximizing a concave objective function subject to linear constraints. This note provides an independent proof of this latter result in a setting slightly more general than the one considered by Fisher. We allow for a technology to convert resources that an economy may be initially endowed with into consumable goods. While shadow price of the resources is a byproduct of our analysis, we are able to obtain the existence of equilibrium prices of the consumable goods by solving a concave-linear optimization problem, whose objective function is similar to the ones considered by Eisenberg and Gale [1959] and Eisenberg [1961].

Structure of consumption sets and existence of equilibria in infinite-dimensional spaces

The price supportability of Pareto optima and existence of competitive equilibrium are established when consumption sets as well as preferences are uniformly proper consumption sets can be different from the non-negative cone. A sufficient condition for uniform properness of a consumption set is that it be the upper-contour set of a well behaved function. Bewley’s (1972) theorem on the existence of equilibrium prices in L’ is also extended by allowing for somewhat more genera1 consumption sets. A class of examples is given to demonstrate the need for some restrictions on the structure of consumption sets.