Game and Auction Theory for Data Scientists

Part 5 of 6: Auction Formats, Bidding and Revenue Equivalence, how to bid when the price depends on what others bid, why the format of an auction matters less for revenue than it seems, and where the winner’s curse turns up outside auctions. Python code provided.

Diogo Ribeiro is a mathematician, researcher and lecturer at the Faculdade de Media Artes e Design, Universidade Técnica do Porto. ORCID 0009–0001–2022–7072. GitHub diogoribeiro7. Gitlab diogoribeiro7.

Part 4 ended with a small bidding game: several bidders, each knowing only their own value for an object, each choosing a bid. This part takes that game seriously.

An auction is a way of selling something when the seller does not know what it is worth to the buyers. The private information that caused so much trouble in Part 4 is the reason auctions exist. They are also where many data scientists meet game theory in production, on one side or the other of an advertising exchange or a procurement process.

The part has three movements. First, the standard formats and how to bid in them, with a result that surprises on first contact: under a set of clean assumptions, formats with very different rules give the seller the same expected revenue. Second, what happens when those assumptions are dropped, where in my simulations the…