Equilibrium transport with time-inconsistent costs

Understand

Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting.

• Motivating examples are nonlinear objectives, state-dependent costs, and regularized optimal transport with general $f$-divergence.
• Under the bicausal constraint, we introduce the concept of equilibrium transport.
• Existence is proved in the semi-discrete Markovian case and the continuous non-Markovian case with strict quasiconvexity, while uniqueness also holds in the second case.