Tradable credit schemes on networks with mixed equilibrium behaviors

Fang He, Yafeng Yin*, Nima Shirmohammadi, Yu Marco Nie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


This paper analyzes and designs tradable credit schemes on networks with two types of players, namely, a finite number of Cournot-Nash (CN) players and an infinite number of (infinitesimal) Wardrop-equilibrium (WE) players. We first show that there are nonnegative anonymous credit schemes that yield system optimum, when transaction costs are not considered. We then analyze how transaction costs would affect the trading and route-choice behaviors of both CN and WE players, and discuss the equilibrium conditions on the coupled credit market and transportation network in the presence of transaction costs. A variational inequality is formulated to describe the equilibrium and is subsequently applied to a numerical example to assess the impacts of transaction costs on a tradable credit system. As expected, transaction costs reduce the trading volume of credits and change their market price. They also change the way how players respond to credit charges in their route choices and cause efficiency losses to the credit schemes that are previously designed without considering transaction costs. With transaction costs, travel costs of WE players will likely increase while those of CN players may decrease due to their higher adaptability in routing strategies.

Original languageEnglish (US)
Pages (from-to)47-65
Number of pages19
JournalTransportation Research Part B: Methodological
StatePublished - Nov 2013


  • Cournot-Nash players
  • Mixed equilibrium
  • Tradable credits
  • Transaction costs
  • Wardrop equilibrium

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation


Dive into the research topics of 'Tradable credit schemes on networks with mixed equilibrium behaviors'. Together they form a unique fingerprint.

Cite this