Congestion on risky routes with risk adverse drivers
We study the impact of information on risk adverse drivers who maximize their von Neumann and Morgerstern expected utility (rather than minimizing expected travel time). The preferences of the users are described by their utility functions. Beside the (potentially inconsistent) mean variance model used so far in transportation, we consider three other standard utility functions: the mean standard deviation model, and the CARA and CRRA utility functions. We show that maximization of expected utility provides a more general formulation than minimization of expected travel time (the latter case corresponds to the standard Wardrop principle). We illustrate the proposed approach with a simple network which consists in one origin/one destination and two routes in parallel. Total demand is inelastic. Capacity on one route is constant and on the other route it is stochastic, and depends on the states of nature, with two possible values. We assume that all users have the same value of time but that they differ in their risk aversion parameter. Equilibrium travel time then depends on the distribution of risk aversion. We consider two polar information regimes: no information and full information. We study the differential impacts of information according to the level of risk aversion, and compute the social value of information. We introduce a formula to compute the value of information that is the individual willingness to pay for information (or in economic terms, the compensating variation). Moreover, we find that optimal route choice may depend on global factors (and not only on local traffic conditions). This has serious implications on the design of driver information systems. Finally, we study road pricing when users are risk neutral (and minimize the expected travel time) and when users are risk adverse. We compare the level of tolls, as well as the benefits of road pricing with and without taking into account risk aversion.
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