Wardrop Equilibrium Can Be Boundedly Rational: A New Behavioral Theory of Route Choice
CoRR(2023)
摘要
As one of the most fundamental concepts in transportation science, Wardrop
equilibrium (WE) has always had a relatively weak behavioral underpinning. To
strengthen this foundation, one must reckon with bounded rationality in human
decision-making processes, such as the lack of accurate information, limited
computing power, and sub-optimal choices. This retreat from behavioral
perfectionism in the literature, however, was typically accompanied by a
conceptual modification of WE. Here, we show that giving up perfect rationality
need not force a departure from WE. On the contrary, WE can be reached with
global stability in a routing game played by boundedly rational travelers. We
achieve this result by developing a day-to-day (DTD) dynamical model that
mimics how travelers gradually adjust their route valuations, hence choice
probabilities, based on past experiences. Our model, called cumulative logit
(CumLog), resembles the classical DTD models but makes a crucial change:
whereas the classical models assume routes are valued based on the cost
averaged over historical data, ours values the routes based on the cost
accumulated. To describe route choice behaviors, the CumLog model only uses two
parameters, one accounting for the rate at which the future route cost is
discounted in the valuation relative to the past ones and the other describing
the sensitivity of route choice probabilities to valuation differences. We
prove tha CumLog always converges to WE, regardless of the initial point, as
long as the behavioral parameters satisfy certain mild conditions. Our theory
thus upholds WE's role as a benchmark in transportation systems analysis. It
also resolves the theoretical challenge posed by Harsanyi's instability problem
by explaining why equally good routes at WE are selected with different
probabilities.
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关键词
new behavioral theory
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