Previously, Akamatsu et al. proposed tradable bottleneck permits as a new transportation demand management scheme and proved the efficiency thereof for a general network. To implement such a scheme, we propose a multi-agent system for general transportation networks. The aim of this system is to achieve a socially optimal state in which the total transportation cost is minimized by the decentralized behaviour of agents. As a concrete step in designing the proposed system, we first define the micro behaviour of the agents. We also assume that the trading markets for bottleneck permits are described by a ttonnement process. We then derive day-to-day dynamics of aggregated traffic flows and permit prices. By analyzing the macro dynamics, we prove that the mean dynamics of the aggregated variables (flows and permit prices) converge to a socially optimal state.