The Declining Price Anomaly is not Universal in Multi-Buyer Sequential Auctions (but almost is)

by   Vishnu V. Narayan, et al.

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 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 non-monotonic 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 non-monotonic price trajectories are extremely rare. In over six million experiments only a 0.000183 proportion of the instances violated the declining price anomaly.


page 1

page 2

page 3

page 4


Two-Buyer Sequential Multiunit Auctions with No Overbidding

We study equilibria in two-buyer sequential second-price (or first-price...

Complexity of Equilibria in First-Price Auctions under General Tie-Breaking Rules

We study the complexity of finding an approximate (pure) Bayesian Nash e...

The Price of Anarchy of Two-Buyer Sequential Multiunit Auctions

We study the efficiency of sequential multiunit auctions with two-buyers...

Simultaneous 2nd Price Item Auctions with No-Underbidding

We study the price of anarchy (PoA) of simultaneous 2nd price auctions (...

Pacing Equilibrium in First-Price Auction Markets

In ad auctions--the prevalent monetization mechanism of Internet compani...

Efficiency of non-truthful auctions under auto-bidding

Auto-bidding is now widely adopted as an interface between advertisers a...

Expanding Multi-Market Monopoly and Nonconcavity in the Value of Information

In this paper I investigate a Bayesian inverse problem in the specific s...

Please sign up or login with your details

Forgot password? Click here to reset