Stackelberg games and multiple equilibrium behaviors on networks
The classical Wardropian principle assumes that users minimize either individual travel cost or overall system cost. Unlike the pure Wardropian equilibrium, there might be in reality both competition and cooperation among users, typically when there exist oligopoly Cournot-Nash (CN) firms. In this paper, we first formulate a mixed behavior network equilibrium model as variational inequalities (VI) that simultaneously describe the routing behaviors of user equilibrium (UE), system optimum (SO) and CN players, each player is presumed to make routing decision given knowledge of the routing strategies of other players. After examining the existence and uniqueness of solutions, the diagonalization approach is applied to find a mixed behavior equilibrium solution. We then present a Stackelberg routing game on the network in which the SO player is the leader and the UE and CN players are the followers. The UE and CN players route their flows in a mixed equilibrium behavior given the SO player's routing strategy. In contrast, the SO player, realizing how the UE and CN players react to the given strategy, routes its flows to minimize total system travel cost. The Stackelberg game of network flow routing is formulated as a mathematical program with equilibrium constraints (MPEC). Using a marginal function approach, the MPEC is transformed into an equivalent, continuously differentiable single-level optimization problem, where the lower level VI is represented by a differentiable gap function constraint. The augmented Lagrangian method is then used to solve the resulting single-level optimization problem. Some numerical examples are presented to demonstrate the proposed models and algorithms.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 41 (2007)
Issue (Month): 8 (October)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Yang, Hai, 1998. "Multiple equilibrium behaviors and advanced traveler information systems with endogenous market penetration," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 205-218, April.
- Yang, Hai & Zhang, Xiaoning & Meng, Qiang, 2004. "Modeling private highways in networks with entry-exit based toll charges," Transportation Research Part B: Methodological, Elsevier, vol. 38(3), pages 191-213, March.
- Meng, Q. & Yang, H. & Bell, M. G. H., 2001. "An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 35(1), pages 83-105, January.
- Devarajan, Shantayanan, 1981. "A note of network equilibrium and noncooperative games," Transportation Research Part B: Methodological, Elsevier, vol. 15(6), pages 421-426, December.
When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:41:y:2007:i:8:p:841-861. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.