Characterizations of pseudomonotone maps and economic equilibrium

By L. Brighi, Reinhard John. 2002

15 citations recorded by the source corpus.

Abstract The paper surveys some recent contributions to the analysis of pseudomonotone maps and their application to economics. It is shown that the concept of pseudomonotonicity is strongly related to a notion of rationality of consumer behaviour which is well known in economics as a weak version of the Weak Axiom of Revealed Preference. In economic models of general equilibrium, a pseudomonotone aggregate excess demand function is seen to guarantee convexity of the set of price equilibria and, in the case of so-called regular economies, even the uniqueness of equilibrium. Some general characterizations of differentiable pseudomonotone maps, which reduce to necessary and sufficient first order conditions under the assumption of regularity, are provided. These conditions are employed in order to prove pseudomonotonicity of aggregate excess demand in economies displaying a particular kind of heterogeneous consumer behaviour.

Subfields: Economics and Econometrics, Management Science and Operations Research, Optimization & Training, Economics & Operations Research

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Management Science and Operations Research

In Optimization & Training

In Economics & Operations Research

Citations in the corpus

Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity (2021, background): “…the non-monotone subsets of quasi-strong monotonicity (a.k.a., strongly pseudomonotone), have many real applications in competitive exchange economy [Brighi and John, 2002], fractional programming [Elizarov and Kalimullina, 2009, Rousseau et al., 2005], and product pricing [Choi et al., 1990].”
Optimistic Dual Extrapolation for Coherent Non-monotone Variational Inequalities (2021, background): “, pseudomonotone and strongly pseudomonotone respectively, also have many real applications in competitive exchange economy [2], fractional programming [10, 37], and product pricing [5].”
Optimal stochastic extragradient schemes for pseudomonotone stochastic variational inequality problems and their variants (2014, background): “e motivation for weakening the monotonicity requirement. 1.1 Motivation We draw motivation from three classes of problems: (a) Competitive exchange economy. We consider a competitive exchange economy [3] in which there is a collection of ngoods with an associated price vector p2Rn ++ and a positive ”