Sequential Auctions with Multi-Unit Demands

Rodriguez, Gustavo E.

doi:10.2202/1935-1704.1534

Cited by 14 publications

(9 citation statements)

References 8 publications

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“…Of course, it is perhaps unreasonable to assume that subgame equilibria arise in practice; we remark, though, that the use of simple bidding algorithms by bidders may also lead to weakly decreasing prices in a multi-buyer sequential auction. For example, Rodriguez [25] presents a method called the residual monopsonist procedure inducing this property.…”

Section: Results and Overview Of The Papermentioning

confidence: 99%

The Declining Price Anomaly Is Not Universal in Multi-buyer Sequential Auctions (But Almost Is)

Narayan

Prebet

Vetta

2019

Algorithmic Game Theory

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The declining price anomaly states that the price weakly decreases when multiple copies of an item are sold sequentially over time. The anomaly has been observed in a plethora of practical applications. On the theoretical side, Gale and Stegeman [11] proved that the anomaly is guaranteed to hold in full information sequential auctions with exactly two buyers. We prove that the declining price anomaly is not guaranteed in full information sequential auctions with three or more buyers. This result applies to both first-price and second-price sequential auctions. Moreover, it applies regardless of the tie-breaking rule used to generate equilibria in these sequential auctions. To prove this result we provide a refined treatment of subgame perfect equilibria that survive the iterative deletion of weakly dominated strategies and use this framework to experimentally generate a very large number of random sequential auction instances. In particular, our experiments produce an instance with three bidders and eight items that, for a specific tie-breaking rule, induces a nonmonotonic price trajectory. Theoretic analyses are then applied to show that this instance can be used to prove that for every possible tie-breaking rule there is a sequential auction on which it induces a non-monotonic price trajectory. On the other hand, our experiments show that nonmonotonic price trajectories are extremely rare. In over six million experiments only a 0.000183 proportion of the instances violated the declining price anomaly. 1 If the values are affiliated then prices can have an upwards drift.

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Section: Results and Overview Of The Papermentioning

confidence: 99%

The Declining Price Anomaly Is Not Universal in Multi-buyer Sequential Auctions (But Almost Is)

Narayan

Prebet

Vetta

2019

Algorithmic Game Theory

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“…This was extended to multi-buyer sequential auctions by Paes Leme et al [12] (see also [13]). Rodriguez [14] studied equilibria in the special case of identical items and identical buyers with endowments.…”

Section: Related Workmentioning

confidence: 99%

Two-Buyer Sequential Multiunit Auctions with No Overbidding

Ahunbay

Lucier

Vetta

2020

Algorithmic Game Theory

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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 nooverbidding 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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“…Several papers (e.g. [11,28]) study the case of two bidders. In the case of two bidders they show that there is a unique subgame perfect equilibrium that survives the iterated elimination of weakly dominated strategies, which is not the case for more than two bidders.…”

Section: Related Workmentioning

confidence: 99%

Sequential Auctions and Externalities

Leme

Syrgkanis

Tardos

2012

Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms

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In many settings agents participate in multiple different auctions that are not necessarily implemented simultaneously. Future opportunities affect strategic considerations of the players in each auction, introducing externalities. Motivated by this consideration, we study a setting of a market of buyers and sellers, where each seller holds one item, bidders have combinatorial valuations and sellers hold item auctions sequentially.Our results are qualitatively different from those of simultaneous auctions, proving that simultaneity is a crucial aspect of previous work. We prove that if sellers hold sequential first price auctions then for unit-demand bidders (matching market) every subgame perfect equilibrium achieves at least half of the optimal social welfare, while for submodular bidders or when second price auctions are used, the social welfare can be arbitrarily worse than the optimal. We also show that a first price sequential auction for buying or selling a base of a matroid is always efficient, and implements the VCG outcome.An important tool in our analysis is studying first and second price auctions with externalities (bidders have valuations for each possible winner outcome), which can be of independent interest. We show that a Pure Nash Equilibrium always exists in a first price auction with externalities.

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Sequential Auctions with Multi-Unit Demands

Cited by 14 publications

References 8 publications

The Declining Price Anomaly Is Not Universal in Multi-buyer Sequential Auctions (But Almost Is)

The Declining Price Anomaly Is Not Universal in Multi-buyer Sequential Auctions (But Almost Is)

Two-Buyer Sequential Multiunit Auctions with No Overbidding

Sequential Auctions and Externalities

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