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Optimistic-Conservative Bidding in Sequential Auctions

In this work we consider selling items using a sequential first price auction mechanism. We generalize the assumption of conservative bidding to extensive form games (henceforth optimistic conservative bidding), and show that for both linear and unit demand valuations, the only pure subgame perfect equilibrium where buyers are bidding in an optimistic conservative manner is the minimal Walrasian equilibrium. In addition, we show examples where without the requirement of conservative bidding, subgame perfect equilibria can admit a variety of unlikely predictions, including high price of anarchy and low revenue in markets composed of additive bidders, equilibria which elicit all the surplus as revenue, and more. We also show that the order in which the items are sold can influence the outcome.