Structural leverage and fictitious play in sequential auctions

Abstract

We model sequential, sealed-bid auctions as a sequential game with imperfect and incomplete information. We develop an agent that, through fictitious play, constructs a policy for the auctions that takes advantage of information learned in the early stages of the game, and is flexible with respect to assumptions about the other bidders' valuations. Because the straightforward expansion of the incomplete information game is intractable, we develop more concise representations that take advantage of the sequential auctions' natural structure. We examine the performance of our agent versus agents that play perfectly, agents that also create policies using Monte-Carlo, and agents that play myopically. The technique performs quite well in these empirical studies, though the tractable problem size is still quite small.