Reference-Dependent Stochastic User Equilibrium with Endogenous Reference Points

Abstract

We consider the application of reference-dependent consumer choice theory to traffic assignment on transportation networks. Route choice is modelled based on random utility maximisation with systematic utility embodying loss aversion for the travel time and money expenditure attributes. Stochastic user equilibrium models found in the literature have considered exogenously given reference points. The paper proposes a model where reference points are determined consistently with the equilibrium flows and travel times. The referencedependent stochastic user equilibrium (RDSUE) is defined as the condition where (i) no user can improve her utility by unilaterally changing path, (ii) each user has as reference point the current travel time and the money expenditure of one of the available paths, and (iii) if each user updates the reference point to her current path the observed path flows do not change. These conditions are formally equivalent to a multi-class stochastic equilibrium where each class is associated with a path and has as reference point the current state on the path, and the number of users in each class equals the current flow on the path. The RDSUE is formulated as a fixed point problem in the path flows. Existence of RDSUE is guaranteed under usual assumptions. A heuristic algorithm based on the method of successive averages is proposed to solve the problem. The model is illustrated by two numerical examples, one relates to a two-link network and another to the Nguyen-Dupuit network. A reference-dependent route choice model calibrated on stated preference data is used. The second example serves also to demonstrate the algorithm. The impact on the equilibrium of different assumptions on the degree of loss aversion with respect to the travel time attribute are investigated.