In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...

Almost all existence results in mathematical economics and game theory rely on some type of fixed point theorem. However, in many cases it is much easier to apply an equivalent stationary point theorem. In this survey paper we show for various general equilibrium and game theoretical models the usefulness of the stationary point approach to prove existence of equilibrium. We also consider path ...

A view has emerged which sees Adam Smith’s main contribution to economics in terms of his equilibrium theory. This paper argues that equilibrium economics was neither Smith’s main contribution nor his chief concern. It is true that Smith made a few observations which may be construed as equilibrium economics in some loose sense. For example, his observation that the market price of a commodity ...

Many existence problems in economics – for example existence of competitive equilibrium in general equilibrium theory, existence of Nash in equilibrium in game theory – can be formulated as fixed point problems. Because of this, theorems giving sufficient conditions for existence of fixed points have played an important role in economics. My treatment is schematic, focusing on only a few repres...

* Correspondence: [email protected] Guizhou Key Laboratory of Economic System Simulation, Guizhou College of Finance and Economics, Guiyang Guizhou 550004, P.R.China Full list of author information is available at the end of the article Abstract In this article, fuzzy bi-directional associative memory neural networks with distributed delays and impulses are considered. Some sufficient conditi...

Equilibrium problems which were introduced by Fan 1 and Blum and Oettli 2 have had a great impact and influence on the development of several branches of pure and applied sciences. It has been shown that the equilibrium problem theory provides a novel and unified treatment of a wide class of problems which arise in economics, finance, image reconstruction, ecology, transportation, network, elas...

We describe competition over space between a competitive shipping industry (truck-barge) and one with market power (the railroad). The latter prices so as to "beat the competition" in equilibrium, or else at the monopoly price, if that is lower. The monopoly price rises more slowly than do the costs of transportation (freight absorption) if the spatial demand at each point is log-concave. With ...

We study the linear Arrow-Debreu’s model and derive a fix point method to find the market equilibrium. The convergence of this method is proved, while the speed is unknown. Besides that, properties about utility distribution and the partition of buyers are also studied. I. PROBLEM DEFINITION The problems of market equilibrium were initially studied in the domain of mathematical economics. We st...