Before revision:  While in the case of commitment, subject to the  truthtelling and participation constraints of the buyer , the seller's problem is a decision problem, in the case of limited commitment, we show that the seller's problem can be represented as an intrapersonal equilibrium, where the different "incarnations" of the seller represent the different beliefs he may have about the buyer's valuation.
After revision:  While in the case of commitment, subject to the truthtelling and participation constraints of the buyer , the seller's problem is a decision problem, in the case of limited commitment, we show that the seller's problem corresponds to an intrapersonal game, where different "incarnations" of the seller represent the different beliefs he may have about the buyer's valuation.