Payoff and Revenue Inequivalence in Repeated Auction with Time-Varying Number of Bidders

Yuma Fujimoto, Kaito Ariu, Kenshi Abe

Keywords: Auction, Revenue Equivalence, Learning in Games, Time-Varying Game

TL;DR: When the number of auction participants varies with time, long-time payoff and revenue become inequivalent between first- and second-price auctions.

Abstract: Ad auctions employ several types of mechanisms, primarily first-price and second-price auctions. One primary question is which mechanism is preferred from the perspective of the payoffs of bidders and the revenue of a seller. An answer is celebrated revenue equivalence, where both the payoff and revenue are equal in equilibrium between different mechanisms. In reality, however, this equilibrium does not always hold, partly because auction environments, such as the number of bidders, vary over time. This study questions whether and how payoff/revenue equivalence is broken by such a time-varying number of bidders. Interestingly, any time-varying number of bidders leads to the loss of payoff for bidders. On the other hand, it can lead to the gain and loss of revenue for the seller, depending on the case. Our theorems can be applied to a broad range of value distributions, including representative examples such as power, exponential, and Pareto distributions. This study advances auction theory by incorporating the perspective of time-varying environments, contributing to auction design in reality, where environmental change is inevitable.

Journal Edition Interest: No

Submission Number: 13