2020 Volume 76 Issue 2 Pages 138-155
In this study, a methodology is proposed to analyze stationary distributions of urban/transportation equilibrium models which would have multiple equilibria due to economies of scale, clearly considering dynamic uncertainty of systems of the models. First, in a framework of continuous time and continuous states, it is clarified that the stationary distribution has a Boltzmann type analytical solution when the urban/transportation equilibrium model can be classified into the potential game and the dynamics of the system follows a specific stochastic process. Second, a method is developed to estimate the stationary distributions with a Markov chain Monte Carlo method. Lastly, the proposed methodology is demonstrated by applying it to a problem to estimate stationary distributions of a spatial agglomeration model, and it is found that the stationary distributions can be estimated with the proposed methodology even if the model has large agents and its stationary distribution cannot be estimated with the existing methodologies.
