Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences under a discrete-time setting. Motivating examples include nonlinear objectives, state-dependent costs, and regularized optimal transport with general $f$-divergence. Under the bi-causal constraint, we introduce equilibrium transport and characterize it with maximum theorem and extended dynamic programming principle. We apply our framework to study the state dependence of two job markets including top-ranking executives and academia. The empirical analysis shows that a job market with a stronger state dependence is less efficient. The University of California (UC) postdoc job market has the strongest state dependence even than that of top executives, while there is no evidence of state dependence on the UC faculty job market. This is a joint work with Erhan Bayraktar.