Bilateral trade with strategic gradual learning

We propose a model of bilateral trade in which private information about the quality of an asset can be acquired only gradually over time. An asset is characterized by a vector of binary i.i.d. attributes, and its worth to a player is equal to a weighted sum of the attributes' values (where weights differ across players). The seller is initially uninformed about the attributes' values, and each period he decides whether to make a price offer or to costlessly inspect an attribute's value. The buyer does not know the attributes' values, but he may or may not observe which inspections were performed (we consider both cases). We study the seller's strategic scheduling of inspections and its effect on the realized gains from trade in equilibrium. We identify the necessary and sufficient conditions under which the players can realize some gains from trade, and all gains from trade.