STOCHASTIC CONVERGENCE OF A HYBRID SCHEME OF TRADABLE BOTTLENECK PERMITS AND CONGESTION PRICING

Akamatsu et al. (2006, 2007a, b) proposed a new dynamic traffic congestion control scheme called "tradable bottleneck permits" (TBP). To mitigate both queuing congestion and flow congestion, Wada and Akamatsu (2010a, b) developed a hybrid scheme combining TBP and congestion pricing, and proved its efficiency properties in a deterministic situation. The present study examined an evolutionary mechanism for implementing the hybrid scheme in a stochastic environment. On the assumption that users' behavior can be modeled with a stochastic learning model (stochastic fictitious play), we first describe a mechanism consisting of trading rules for the TBP market and users' behavior. We then derive a stochastic dynamics of the learning process from this mechanism. Finally, we show that the stochastic dynamics converges to an equilibrium state, and that user assignment at equilibrium is efficient in the sense that social surplus is maximized.