Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.trb.2007.03.002
Title: Stackelberg games and multiple equilibrium behaviors on networks
Authors: Yang, H.
Zhang, X.
Meng, Q. 
Keywords: Marginal function
Mixed equilibrium
Network optimization
Stackelberg game
Variational inequalities
Issue Date: Oct-2007
Citation: Yang, H., Zhang, X., Meng, Q. (2007-10). Stackelberg games and multiple equilibrium behaviors on networks. Transportation Research Part B: Methodological 41 (8) : 841-861. ScholarBank@NUS Repository. https://doi.org/10.1016/j.trb.2007.03.002
Abstract: 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. © 2007 Elsevier Ltd. All rights reserved.
Source Title: Transportation Research Part B: Methodological
URI: http://scholarbank.nus.edu.sg/handle/10635/66196
ISSN: 01912615
DOI: 10.1016/j.trb.2007.03.002
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