EconPapers    
Economics at your fingertips  
 

Heterogeneity and chaos in congestion games

Ahmad Naimzada () and Roberto Raimondo

Applied Mathematics and Computation, 2018, vol. 335, issue C, 278-291

Abstract: We analyze a class of congestion games where agents use resources to send a finite amount of goods from an initial location to a terminal one. The resources are costly and costs are load dependent. In this context we concentrate on the heterogeneity because we not only assume that agents have limited computational capability but also they differ in the quantities they must send and the reactivity. We introduce an appropriate dynamical system, which has the steady state exactly at the unique Nash equilibrium of the static congestion game, and we investigate the dynamical behavior of the game. We provide a closed form characterization on the unique Nash equilibrium in the underlying static congestion game and we prove that the equilibrium crucially depends on the aggregate congestion. Not only do we provide a local stability condition in terms of the agents’ reactivity and the nonlinearity of the cost functions but also we study the role of the heterogeneity in this context. We show analytically that heterogeneity can be destabilizing with a cascade of flip-bifurcation leading to periodic cycles and finally to chaos but also that mastering the degree of heterogeneity can be used to tame and control complex dynamics; moreover in relation to the reactivity levels their product must roughly small. However if both reactivity levels are near but outside the stability region then it is sufficient to act on just one to restore stability. Finally, if both levels are far form the stability region acting on one will not restore stability.

Keywords: Heterogeneity; Congestion games; Nash equilibrium; Bounded rationality; Bifurcation; Complex dynamics (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318303217
Full text for ScienceDirect subscribers only

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:eee:apmaco:v:335:y:2018:i:c:p:278-291

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Dana Niculescu ().

 
Page updated 2019-08-13
Handle: RePEc:eee:apmaco:v:335:y:2018:i:c:p:278-291