Mean field equilibria of dynamic auctions with learning: A dynamic revenue equivalence theorem

Auctions are observed as a market mechanism in a wide range of economic transactions involving repeated interactions among the market participants: sponsored search markets run by Google and Yahoo!, online marketplaces such as eBay and Amazon, crowdsourcing, etc. In many of these markets, the participants typically have incomplete information; for example, the participants may not know the quality of the good being auctioned or their value for the good. In such settings, repeated interactions among the participants give rise to extremely complex bidder behavior due to the presence of learning among the participants. To study learning, we consider a dynamic setting where identical copies of a good are sold through a sequence of second price auctions over time. Each agent in the market has an independent private valuation which determines the distribution of the reward she obtains from the good. However, the agents are unaware of their own private valuations. Every time an agent wins an auction and obtains a copy of the good, her realized reward from the good informs her about her valuation. Thus, each agent faces a trade-off between exploration (by bidding higher) and exploitation (by bidding close to her expected rewards).