Stochastic User Equilibrium and Value-of-time Analysis with Reference-dependent Route Choice
Reference-dependent theory of riskless choice assumes that carriers of utility are gains and losses relative to a reference point and that individuals are loss averse, i.e. losses are valued more highly than gains. Reference-dependent money measures of the attributes in the utility functions are defined: the willingness to pay, the willingness to accept, the equivalent gain and the equivalent loss. Experimental evidence has been provided which supports reference-dependent theory for riskless route choice. A natural next development is the application of the theory to network analysis. This is an under-researched area. In the paper, the multi-class reference-dependent stochastic user equilibrium (RDSUE) problem under the status-quo assumption for the reference point is formulated. Conditions that guarantee the properties of existence and uniqueness of RDSUE are considered. The property of reflexivity of RDSUE is also considered to verify if the equilibrium is maintained when the reference point is updated to the new status quo. A methodology for the reference-dependent valuation of travel time changes over a network is provided. Data from a survey are used to estimate a reference-dependent route choice model and the attendant reference-dependent values of time. The estimation results are in agreement with econometric literature supporting loss aversion. The application to the case of a town bypass with toll illustrates the reference-dependent approach to network analysis and the implications of its use for policy making. It is shown that, if the interventions on the supply are phased, it is possible to exploit loss aversion and obtain advantages in terms of toll revenues and travel time spent.