Option Values in Sequential Auctions with Time-Varying Valuations

We investigate second-price sequential auctions of unit-demand bidders with time-variable valuations under complete information. We describe how a bidder figures willingness to pay by calculating option values, and show that when bidders bid their option value, and a condition of consistency is fulfilled, a subgame-perfect equilibrium is the result. With no constraints on valuations, equilibria are not necessarily efficient, but we show that when bidder valuations satisfy a certain constraint, an efficient equilibrium always exists. This result may be extended to a model with arrivals of bidders. We show how the equilibrium allocation, bids, and bidder utilities are calculated in the general case. We prove constructively that a pure subgame-perfect equilibrium always exists, and show how all pure equilibria can be found by the method of option values