Evolution Solutions of Equilibrium Problems: A Computational Approach

Monica-Gabriela Cojocaru () and Scott Greenhalgh ()
Additional contact information
Monica-Gabriela Cojocaru: University of Guelph
Scott Greenhalgh: Queen’s University

A chapter in Mathematical Analysis, Approximation Theory and Their Applications, 2016, pp 121-138 from Springer

Abstract: Abstract This paper proposes a computational method to describe evolution solutions of known classes of time-dependent equilibrium problems (such as time-dependent traffic network, market equilibrium or oligopoly problems, and dynamic noncooperative games). Equilibrium solutions for these classes have been studied extensively from both a theoretical (regularity, stability behaviour) and a computational point of view. In this paper we highlight a method to further study the solution set of such problems from a dynamical systems perspective, namely we study their behaviour when they are not in an (market, traffic, financial, etc.) equilibrium state. To this end, we define what is meant by an evolution solution for a time-dependent equilibrium problem and we introduce a computational method for tracking and visualizing evolution solutions using a projected dynamical system defined on a carefully chosen L 2-space. We strengthen our results with various examples.

Keywords: Projected dynamics; Time-dependent equilibrium problems; Dynamic adjustment; Applications (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-31281-1_6

Ordering information: This item can be ordered from
http://www.springer.com/9783319312811

DOI: 10.1007/978-3-319-31281-1_6

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().