I study a dynamic model of durable‐good monopoly where the seller minimizes lifetime regret against the worst‐case type of buyer. The optimal mechanism is time consistent: at no point can the seller benefit from replacing it with another mechanism. Despite this, the optimal mechanism cannot be supported in an equilibrium without commitment. This is because the seller's regret is endogenously determined by the best counterfactual payoffs he can obtain against every type, and these payoffs vary with his commitment power. When the seller lacks commitment, the good may not be sold to all types. However, in the limit as offers become frequent, the good is sold immediately at a price equal to the lowest buyer value.
Rumen Kostadinov (Thu,) studied this question.