Abstract
We study equilibria in two-buyer sequential second-price (or first-price) auctions for identical goods. Buyers have weakly decreasing incremental values, and we make a behavioural no-overbidding assumption: the buyers do not bid above their incremental values. Structurally, we show equilibria are intrinsically linked to a greedy bidding strategy. We then prove three results. First, any equilibrium consists of three phases: a competitive phase, a competition reduction phase and a monopsony phase. In particular, there is a time after which one buyer exhibits monopsonistic behaviours. Second, the declining price anomaly holds: prices weakly decrease over time at any equilibrium in the no-overbidding game, a fact previously known for equilibria with overbidding. Third, the price of anarchy of the sequential auction is exactly \(1 - 1/e\).
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Notes
- 1.
We present our results for second-price auctions. Given an appropriate formulation of the bidding space to ensure the existence of an equilibrium [12] these results also extend to the case of first-price auctions.
- 2.
The exposure problem arises when a buyer has large value for a set S of items but much less value for strict subsets of S. Thus bidding for the items of S sold early in the auction exposes the buyer to a high risk if he fails to win the later items of S.
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Acknowledgements
We are very grateful to Rakesh Vohra for discussions on this topic. We thank the referees for their helpful comments and suggestions.
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Ahunbay, M.Ş., Lucier, B., Vetta, A. (2020). Two-Buyer Sequential Multiunit Auctions with No Overbidding. In: Harks, T., Klimm, M. (eds) Algorithmic Game Theory. SAGT 2020. Lecture Notes in Computer Science(), vol 12283. Springer, Cham. https://doi.org/10.1007/978-3-030-57980-7_1
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