A Simple Selling and Buying Procedure

For the assignment game, we anlayze the following mechanism: sellers, simultaneously, fix their prices first, then buyers, sequentially, decide which object to buy, if any, among the remaining objects. The first phase of the game determines the potential proces, while the second phase determines the actual matching. We prove that the set of subgame perfect equilibria in pure strategies in the strong sense of the mechanism coincides with the set of sellers' optimal stable outcomes when buyers use maximal strategies.