A bi-level model of the relationship between transport and residential location Justin Sueun Chang a, * , Roger Laurence Mackett b a Korea Transport Institute, 2311 Daehwa-Dong, Ilsan-Gu, Goyan City, Gyonggi-Do 411-701, Republic of Korea b Centre for Transport Studies, University College London, Gower Street, London WC1E 6BT, UK Received 20 March 2003; received in revised form 10 January 2005; accepted 21 February 2005 Abstract Thispaperexploresabid-rentnetworkequilibriummodelwhichrepresentstherelationshipbetweentrans- port and residential location. The relationship is examined in terms of the competition of decision-makers for locations. The model discusses difficulties in addressing the characteristics of locations, particularly hetero- geneity and indivisibility. A hedonic interpretation is included as a way to resolve these challenges. The model investigates the process in which households make their decisions. This process is shown as an n-player non- cooperative game, following the Nash equilibrium for this game, which is defined as well. The game is accompanied by the systematic interactions between transport and land-use. A mutual adjustment process represents these interactions. The three components are structured by a bi-level mathematical program. The final formulation is interpreted as an oligopolistic Cournot game of which consequence is an approxima- tion of the n-player non-cooperative game. The functional relationship between the decision variables of the upper and the lower levels of the bi-level program produces endogenously-determined transport impedance and locational attractiveness. The endogenous network performance indices of the model are expected to overcomethelackofarealisticnetworkequilibriumdescriptionintheexistingmodels.Apath-basedheuristic algorithm and a simple numerical example are presented. Finally, some concluding remarks are given. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Oligopoly; Cournot game; Nash; Bid-rent; Network equilibrium; Bi-level 0191-2615/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.trb.2005.02.002 * Corresponding author. Tel.: +82 31 910 3061; fax: +82 31 910 3225. E-mail address: justin@koti.re.kr (J.S. Chang). www.elsevier.com/locate/trb Transportation Research Part B 40 (2006) 123–146