Abstract
This paper characterizes the perfect Bayesian equilibrium in an ascending price package auction. Bidders play history-dependent strategies in an ascending auction, and we show that it leads to serious underbidding. We suppose that there are 2 objects and 3 bidders: 2 local and 1 global bidders. The local bidders want only one unit of the goods, while the global bidder wants both. We show that either of the 2 local bidders stops bidding at the beginning. Although local bidders generally face the threshold problem and have incentives to underbid, once a bidder becomes a unique remaining local bidder, he/she bids truthfully after that subgame. This implies that stopping early by a local bidder makes the remaining bidder behave aggressively and truthfully. Hence, each local bidder wants to stop bidding earlier than the other and a race for a “free-riding seat” arises. The equilibrium outcome is unique under some conditions.
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